Friday, August 14, 2020

Grace of God

 Many religions, in connection with the doctrine of the forgiveness of sins, speak about Grace of God. Allegedly, God, “out of love”, forgives man all his sins – all he needs to do is to sincerely regret and confess them. This attitude, however, mistakes God’s love for weakness and completely denies the Divine justice. According to the Law of Reciprocal Action, everything, good or bad, returns back to man. Nothing can be forgiven, but all must be paid until the last penny. As it says in the Bible, a good tree will produce good fruit and a bad tree will produce bad fruit, no matter we like it or not, whether we believe it or not.

Let’s see how such “forgiveness of sins” looks like in practice. Man is thinking about what he’s done a couple of minutes and then he “regrets” his deeds. And thereby he considers the whole thing terminated. He does not try to make any effort to change his inner self. Why would he do it? After all, he was told to only regret and eventually to say a few prayers as a sign of repentance – and the Grace of God should put everything back in order. Such a pity is only a deceptive appeasement of conscience and has no real effect. Confessionals are still full of sinners and man does the same unpleasant things over and over again, often during his whole life.\r\nThe usual act of regretting sins does not work primarily because just then man deals with his past, although, recent acts; so basically he is thinking about how he was, not how he is. The bad personality traits that led him to the wrong doing and which must be removed, are still present in him, not in the past. The past is only a memory of our mind, not a tangible reality, in which we can feel and change anything. Therefore, man is almost always able to continue acting the same wrong way no matter he believes in “God’s Grace” and confesses. As long as he is not seeking the way to get rid of his personality flaws and instead of doing so, he is dealing with a “dead” past, he cannot succeed. Thinking about past acts is only good for better self-knowledge, so that we know how we are and what we need to change inside ourselves in the present. Excessive thinking and dwelling on the past would distract us from life in the present, keep us depressed from seeing who we once were and thus darken us even more.

The real change must take place within us, not within our thoughts. Regretful thoughts are too shallow to touch the spirit and change something on human nature. If man wants to change, he has to feel the existing disharmony inside him in his heart. It is not enough to know that he acted improperly – he must imminently feel this improperness within himself. Feel so truly and deeply that he will never be able to do anything like that again, because he will feel disgust towards such deeds from the depth of his soul. Knowing the truth about what wrongful acting causes must be simply stronger than the sweet desire to sin. Only then is it possible to receive the gift of God’s Grace.\r\nEven if the promised forgiveness really worked, there would be still one more serious fact, which is, while relying on “all forgiving Grace of God”, often forgotten – man did not make the due amends for the damage he had caused by his misconduct. And that is the moment when real God’s Grace can be applied.

In order to understand correctly in what the Grace of God consists of, it is necessary to be aware of the existing Divine laws, which determine the way how the forces in the Creation interact. According to one of these laws, only the forces of the same kind can affect each other.

You are certainly familiar with the manifestation of this law in the material world: you cannot drill a hole into the water; you cannot bend the air with hammer thumps, you cannot catch the radio waves with a butterfly net; etc., because these elements have different nature. Similarly, this law is also applied in the spiritual realm, where it allows interaction only between forces of the same kind. Thus, any injustice, which would occur in the interaction between heterogeneous forces, is ruled out beforehand. Superior kind would always completely dominate just as if, for example, lightweight and heavyweight athletes or professionals and amateurs competed with each other.\r\nNow, let’s take a look at how this law applies to the human deeds:\r\nImagine two people who, long ago, intentionally harmed someone’s health. Let’s suppose that one of them realized the wrongness of his actions and changed himself; the other one, however, did not, and has even defined his actions as the law of the strongest, having considered them right. Regardless how he justified his own actions, the harm he has caused will return back to him. In addition to pain, mockery and limited life opportunities of the harmed person, there are also the worsened life conditions of harmed person’s family which must be added to the consequences of the harm. For example, due to the lack of funds, his children might be deprived from the opportunity of living their childhood fully, of having the desired education, which may bring another negative consequences charged to the account of the man who has caused the harm in the first place. And we cannot even imagine how many similar negative consequences are related to wrong acts. The harvest of human deeds is usually much greater than the seeds we sowed; in a similar way to the mustard seeds that give rise to several meters tall plants whose seeds grow into another and another plants.\r\nHow will the reverse effect of those deeds look inside such different people? The one who saw his act as wrong and changed himself to a better person is now radiating light and bright vibrations, to which heavy and dark vibrations, returning due to his previous deeds, cannot lean. The bad effects will hit him only with reduced force, proportionally to how much of the dark vibrations he removed from his personality. In case that no darkness is found inside him, the bad effects will just miss him. Unlike him, the man who did not change himself will be hit with full force by the returning effects of his erstwhile deed, because these returning dark vibrations will find inside him full support for their activities. The effect will be huge and the man will probably end up in a wheelchair. Alas, if he has not managed to realize what his behavior had caused and continued to act ruthlessly! He must experience himself the harm he caused to others.

The Law of Uniformity protects people from unnecessary suffering by allowing encounters only between forces of the same kind. Why should the man who has already changed himself suffer for his past acts? It would not bring him any benefit. It would be only a sign of imperfection, which is excluded from the perfect Divine laws. Suffering is necessary only for obdurate people who are unable to recognize wrongness of their actions other than by experiencing the evil they caused for themselves.\r\nIf man is conceited, calculating, selfish, malicious, or has other dark traits within himself, his spiritual body will radiate the darkness as well. It will consist of heavy and dense vibrations and anything really good won’t be able to reach him. Conversely, man who is generous, friendly, noble-minded, well-meaning... will radiate gentle and light vibrations of bright vivid colors. He will be open to only equally bright and beautiful forces and anything dark will not be able to hurt him seriously. If such different people meet together, they will not find common ground easily. Therefore, everyone seeks intuitively his kind of people in accordance with the Law of Uniformity.\r\nGod’s Grace is never given to those who admitted their guilt, regretted their acts and wanted to change themselves, but it is given only to those who actually changed themselves. God’s Grace “recognizes” such man according to how he radiates. It works in perfect Divine laws according to how intense is man’s light or darkness, not according to what he thinks of himself. Thinking about wrongdoing does not make spirit bright and thus it does not prevent the effect of returning dark harvest. Only there, where the spirit is not surrounded by dark radiation, but where its robe is cleaned, returning effects of past bad acts cannot find any support and “forgiveness of sins” occurs.

This is the way the Grace of God works in our lives. Even the greatest sinner can step up to the Light without having to worry about reverse effects of his past deeds crushing him down even if these effects were extremely huge. The Grace of God consists only in this – not in a go-as-you-please forgiveness of sins for which God’s Grace is incorrectly considered.

In relation to the laws, in which the Grace of God applies, it remains to be said that whereas on one hand these laws help people to overcome the consequences of their bad deeds (so called “karma”), on the other hand they also work vice versa. If man falls spiritually and his astral bodies become dark and heavy, he thus stops returning effects of his erstwhile good deeds. Good effects will not be able to hold on to dark vibrations just as effects of his bad deeds would not be able to hit him when he changed for the better and radiated brightly.\r\nThe Law of Uniformity and the Law of Reciprocal Action lead us back to the life in the present, and the Grace of God is given to us as a huge help on our way to the Light. It does not matter what was in the past, but only how we behave now matters.

Who we are and how we radiate can not be pretended or obtained otherwise than by honest work on ourselves. Knowledge that our past faults, even the worst ones, do not stand between us, and the Light opens the way to the Light for everyone who is willing to find out what they are doing wrong and to do their best to change themselves. The Grace of God will assist them.

In the Light of Truth

 Anything of true value can never be gained without a great deal of effort. This is true especially when seeking the Truth and real knowledge, because Truth and real knowledge are anything but cheap clichés and the smooth talk that is often mistaken for real knowledge.

The work In the Light of Truth enables us to learn unspoiled and simple Truth through its perfect description of the whole of Creation and the functioning of its Universal Laws. Specifically we can find there the clear and straight path guiding human spirits to self-realization, spiritual development and their return out of this material world back to the spiritual world from where they had descended for the purpose of developing their souls.

Like any other book, the book In the Light of Truth can only point at the Truth, because Truth itself is not expressible in human words and therefore cannot be put into a physical book. Instead it is far more important to live the written word with our spirit than it is to learn rational facts. Only while fully absorbing each sentence and comparing your own life with the natural laws as they will be shown in front of your eyes in their perfection, will the book In the Light of Truth become useful to you. As a matter of fact, any knowledge that offers information only is of no real value, if at the same time it does not lead us to full spiritual consciousness and provides us the ability of differentiating unmistakably and in all situations of our daily lives that which is essential from what is irrelevant, that which is true from what is false, that which is worthy from what is worthless.

If you read the book In the Light of Truth very carefully, and if you were to let each sentence fully come to life within you, then it could happen to you that you might not remember much of it, but everything you feel inside will then have become alive. And you will be able to automatically apply all of it to your life without need to remember how it was written in the book. The Truth will become your own knowledge and you will feel it clearly inside of you without the need of either thinking or meditating about it. The inner voice is the faithful connection between the spirit and the Light and allows you to perceive clearly and every moment of your life what is or what is not in harmony with God's natural laws.

If you have not read the book In the Light of Truth yet, then we would encourage you to read the lectures in this book from the beginning and in the same sequence in which the author has placed them there. This is important, because each lecture brings new information that causes the necessary spiritual growth to occur for readers to then fully comprehend all the new information that is offered in each subsequent lecture.

Reading the book In the Light of Truth is not too easy. Full concentration and spiritual watchfulness is demanded of the reader. But the effort of reading is work on ourselves at the same time and helps us in our spiritual ascent, without which it is impossible to find the Truth.

The book In the Light of Truth does not offer ready-made opinions, instead its author, Abdrushin, encourages us to strictly and objectively examine the knowledge brought by him. However, if it is your intention to contest or criticize the Truth that is contained in the book, or if you want to prove your own opinions and prejudices, or if you wish to make the author the idol or the subject of fanatical following, then you are wasting your time. The book In the Light of Truth is meant for sincere seekers who want to live according to that Truth and who want to return to living in harmony with God's natural laws again.

If you will read the book In the Light of Truth with a real desire for knowledge and without all prejudice and rigid dogmas, then you will find treasure in it that is incomparable to all the treasures of the world. For every seeker the work In the Light of Truth is the best source of knowledge we can recommend. Our web pages are but opaque reflections of the knowledge you can find in that book. If you possess at least a shred of desire for the Truth, then this book will ignite a flame of knowledge in you that will never go extinct.

ARTICLES: KNOWLEDGE Stream of Light

 It is not the most important thing if man is good or bad, but if he or she is, or is not. If you do not believe, remember Paul, who at first pursued and killed Christians, and then became the strongest apostle of Christ; or Jesus' words "...the publicans and the harlots go into the kingdom of God before you". Bad man can easily find the Truth and become good. But if somebody is empty within himself, acting like "a good boy" does not help him to develop spiritual consciousness. In order for man to exist, he must be spiritually alive and the Light must flow through his beingness. To wear the mask of goodness, which is by mistake just replaced with silkiness, is not enough.

The stream of Light in man is often blocked by various qualities - self-interestedness, hypocrisy, insincerity, complexes... The more such blocks we deal with, the more the stream of Light is under restriction, which actually flows to all human beings with equal measure. Therefore, the saying that God loves all the creatures without exception is truth.

Every block that stays in the Light's way is created by our own energies - they unfriendly stand against the Light - it is, for example, vanity, fear, envy... The less quantity of the blocks is in man, the more is he vital and capable to perceive the reality by spirit. In order to achieve the full flow of the Light, man does not need to do anything; it is enough if he stops doing things which are blocking the stream of the Light flowing to him.

If man had a belief - which is the same thing as not resisting to the Light (if he stopped having fears, prejudges, narrow-minded opinions...), he would irradiate nicer glow and would immediately attract other similar - beautiful life situations... Therefore, it is truth that belief makes miracles. The more lighter is man and the more brighter within himself, the more he can perceive by his spirit; then the real spiritual way of life opens before him, which is not replaceable by any read or learned information.


Wednesday, August 12, 2020

Hospitals afire: on lack of safety in health-care centres

 

Health-care centres lack fire safety because governments pay lip service to regulation


he shocking deaths of at least 19 people in special facilities for COVID-19 management in Vijayawada and Ahmedabad have exposed the deep rot in regulatory processes for institutional and commercial building safety. While 11 died in the Andhra Pradesh incident, where a hotel had been taken over by a private hospital to run a COVID-19 care centre, nine patients perished in the blaze in a Gujarat hospital intensive care unit (ICU). These ghastly incidents which claimed the lives of those who were getting treatment or recovering from an infection in supposedly secure conditions lay bare the lack of preparedness among States to manage the expanding pandemic, and hasty contracting procedures. In a familiar pattern, civic and fire authorities who were expected to monitor the safety of such buildings have sought to pin responsibility for the carnage on the owners of the properties. They are being held responsible for failure to obtain a no objection certificate or, in the case of the hotel-turned-COVID-19 care centre, carrying out electrical upgrades for safety. This is clearly untenable, as the Supreme Court of India observed about a decade ago in the Uphaar cinema fire tragedy case in Delhi, pulling up authorities including the Union Home Ministry for abdicating responsibility and passing the buck on to the management of the institution. In the Ahmedabad ICU blaze, patients expected the institution to offer the highest levels of safety, but suffered as it was ill-equipped to fight a fire.

Safety regulation of buildings used for health-care delivery is a subset of the overall need to regulate hospitals, and States should use the recent deadly fires as the occasion to launch much-delayed reform. In the absence of safety systems, many died of fire and smoke inhalation, while those who survived had nothing but luck to count on. This situation cannot be allowed to continue. The National Building Code of India, with additional fire safety provisions for hospitals, is the basis for hospital accreditation systems, but these should be made mandatory and enforced in all States. If smoke alarms and sprinkler systems, along with local fire-fighting aids are available, loss of life can be eliminated. All patients should also be covered by substantial life insurance. Evacuation systems for ICU patients need to be part of the building design. Often, hospital buildings are regularised for unapproved constructions by State governments acting thoughtlessly. Schemes introduced to regularise building violations are clearly anti-social in character. The many fires in institutional buildings and their terrible toll should lead to a full inspection of all such facilities for safety, with civil society keeping up the pressure on governments to act.

Just closure: On Italian marines case

 

The focus must be on adequate compensation for families of fishermen killed by marines


t may seem pragmatic to keep any pending litigation alive until all dues relating to it are paid and all legal issues are settled. However, it is somewhat puzzling that the Supreme Court of India has said it would keep the Italian marines’ case alive until “hefty” and “adequate” compensation is paid by Italy for the killing of two fishermen by its marines on February 15, 2012. The Court has indicated that it would not allow the closure of the trial until such compensation is paid. And it has ordered that the families of the victims be heard on this matter. Once the Union government has declared that it would abide by the ruling of the Permanent Court of Arbitration (PCA) at The Hague, which granted immunity to the marines and favoured Italy as the appropriate jurisdiction where they could be tried for the crime, it does not seem proper to delay the process of bringing closure to the matter. For one thing, the PCA, an arbitral tribunal that adjudicates disputes under the United Nations Convention on the Law of the Sea (UNCLOS), has itself ruled that India is entitled to compensation for “loss of life, physical harm, material damage to property... and moral harm suffered by” the captain and crew members of St. Antony, the fishing vessel involved, and mandated negotiations on the quantum. Second, it hardly needs emphasis that the pendency of the matter in court should not become a bargaining point that delays the reaching of a fair settlement. Continuing hearings may also be seen as India being reluctant to cease all criminal proceedings against the marines as per the ruling.

The Court’s resolve to obtain adequate and hefty compensation for the families of the victims is welcome, though it would be difficult to have a judicial determination of what quantum would satisfy these requirements. The Centre may have approached the top court for formal permission to close the pending trial proceedings as a matter of abundant caution. But as far as the law goes, it could have approached the trial court itself through the public prosecutor for withdrawal from prosecution under Section 321 of the CrPC. Too many legal tangles have already caused enough diplomatic rupture in the progression of the Enrica Lexie-St. Antony case since 2012. Article 253 of the Constitution, which says Parliament may enact a law to give effect to any international treaty or convention, has been cited to argue that in view of the arbitral court’s finding on jurisdiction being in conflict with the Supreme Court’s ruling in 2013 that the Union government alone can try the case, a law may be needed before the trial is closed. This is just needless quibbling as the conflict has ceased after India agreed to abide by the tribunal’s ruling in keeping with its obligations under UNCLOS. India’s focus should now be on negotiating for compensation and ensuring a purposive criminal trial in Italy.

Rajasthan lessons: On Congress truce

 

If the truce in the Congress is to endure, both factions must mend their ways


The crisis in the Congress in Rajasthan that nearly brought down the government led by Chief Minister Ashok Gehlot has blown over. The group led by Sachin Pilot has reiterated its loyalty to the party, though the stand-off cost him the posts of Deputy Chief Minister and State party chief. The truce is an outcome of the realisation on both sides that their positions had become self-destructive and unsustainable. Mr. Gehlot faced the risk of losing the government, while Mr. Pilot stared at the unnerving prospect of a life outside the Congress. The turmoil in Rajasthan has also been yet another occasion to note with deep concern the tendency of the judiciary to overstep its remit set by law, brazen partisanship of the Governor, and misuse of central agencies to tilt the political balance. The crisis was primarily internal to the Congress, but the Bharatiya Janata Party’s maximalist approach to capture power at all costs was evident. The unseemly power struggle had derailed governance in the State in the midst of a pandemic. Now that a settlement has been reached, the Centre and the State, the Bharatiya Janata Party and all sections within the ruling party must come together to combat the pandemic.

The Congress is facing the most severe crisis in its history and it cannot afford any complacency in keeping its house in order. The party is constantly at the receiving end of the Bharatiya Janata Party’s relentless onslaught and in March it lost the government in Madhya Pradesh, which it had won in 2018 along with Rajasthan and Chhattisgarh. According to Mr. Gehlot’s own admission, there was no communication between him and Mr. Pilot ever since the formation of the government in 2018. That is a sad commentary on the party. Mr. Pilot has said he resorted to rebellion only after his grievances went unheeded. This brinkmanship might have taught them both, and the party’s central leadership, some lessons for the future. The resolution of the crisis took the intervention of former Congress President Rahul Gandhi, who commands the loyalty of both. He could have resolved it earlier or even preempted the crisis altogether. There is no single model for running a political party, but the nature, history and character of the Congress impel it to be consultative and deliberative in its internal and external conduct. As Rajasthan demonstrated, Mr. Gandhi has a role to play in facilitating this. Mr. Gandhi has been focused on building a critique of the Bharatiya Janata Party and its government but such politics will be effective only when reinforced by a strong organisation. He has strong opinions on what the Congress should ideally be, but he has no option but to start with what it currently is.

Tuesday, June 9, 2020

What is the Heisenberg Uncertainty Principle?

Heisenberg Uncertainty Principle Formula and Application
If, ∆x is the error in position measurement and ∆p is the error in the measurement of momentum, then

∆X  ×  ∆p  ≥  \frac{h}{4\pi } 
h
 

Since momentum, p = mv, Heisenberg’s uncertainty principle formula can be alternatively written as-

∆X  ×  ∆mv  ≥  \frac{h}{4\pi } 
h
  or    ∆X  ×  ∆m × ∆v  ≥  \frac{h}{4\pi } 
h
 

Where, ∆V is the error in the measurement of velocity and assuming mass remaining constant during the experiment,

∆X  ×  ∆V  ≥   \frac{h}{4\pi m} 
4πm
h
  .

Accurate measurement of position or momentum automatically indicates larger uncertainty (error) in the measurement of the other quantity.

Applying the Heisenberg principle to an electron in an orbit of an atom, with h = 6.626 ×10-34Js and m= 9.11 ×10-31Kg,

∆X ×  ∆V  ≥ \frac{6.626\times {{10}^{-34}}}{4\times 3.14\times 9.11\times {{10}^{-31}}} 
4×3.14×9.11×10 
−31
 
6.626×10 
−34
 
  = 10-4 m2 s-1.

If the position of the electron is measured accurately to its size (10-10m), then the error in the measurement of its velocity will be equal or larger than 106m or 1000Km.

Heisenberg principle applies to only dual-natured microscopic particles and not to a macroscopic particle whose wave nature is very small.

Also Read: de Broglie Equation

Explaining Heisenberg Uncertainty Principle With An Example
Electromagnetic radiations and microscopic matter waves exhibit a dual nature of mass/ momentum and wave character. Position and velocity/momentum of macroscopic matter waves can be determined accurately, simultaneously. For example, the location and speed of a moving car can be determined at the same time, with minimum error. But, in microscopic particles, it will not be possible to fix the position and measure the velocity/momentum of the particle simultaneously.

An electron in an atom has a mass of 9.91 × 10-31Kg. Naked eyes will not see such small particles. A powerful light may collide with the electron and illuminate it. Illumination helps in identifying and measuring the position of the electron. The collision of the powerful light source, while helping in identification increases the momentum of the electron and makes it move away from the initial position. Thus, when fixing the position, velocity /momentum of the particle would have changed from the original value. Hence when the position is exact, error occurs in the measurement of velocity or momentum. In the same way, the measurement of momentum accurately will change the position.

Hence, at any point in time, either position or momentum can only be measured accurately.

Simultaneous measurement of both of them will have an error in both position and momentum. Heisenberg quantified the error in the measurement of both position and momentum at the same time.

Heisenberg’s γ-ray Microscope
A striking thought experiment illustrating the uncertainty principle is Bohr’s / Heisenberg’s Gamma-ray microscope. To observe a particle, say an electron, we shine it with the light ray of wavelength λ and collect the Compton scattered light in a microscope objective whose diameter subtends an angle θ with the electron as shown in the figure below

Heisenberg’s γ-ray Microscope
The precision with which the electron can be located, Delta x, is defined by the resolving power of the microscope,

sin \theta =\frac{\lambda }{\Delta x}\Rightarrow \Delta x=\frac{\lambda }{sin \theta }sinθ= 
Δx
λ
 ⇒Δx= 
sinθ
λ
 

It appears that by making λ small, that is why we choose γ-ray, and by making sin θ large, Delta x can be made as small as desired. But, according to the uncertainty principle, we can do so only at the expense of our knowledge of x-component of electron momentum.

In order to record the Compton scattered photon by the microscope, the photon must stay in the cone of angle θ and hence its x-component of the momentum can vary within ±(h/λ) sin θ. This implies, the magnitude of the recoil momentum of the electron is uncertain by

\Delta p_{x}=\frac{2h}{\lambda }sin \thetaΔp 
x
 = 
λ
2h
 sinθ

The product of the uncertainty yields,

\Delta x\Delta p_{x}=\frac{\lambda }{sin \theta }\frac{2h}{\lambda }sin \theta =4\pi hΔxΔp 
x
 = 
sinθ
λ
  
λ
2h
 sinθ=4πh

Is Heisenberg’s Uncertainty Principle Noticeable in All Matter Waves?
Heisenberg’s principle is applicable to all matter waves. The measurement error of any two conjugate properties, whose dimensions happen to be joule sec, like position-momentum, time-energy will be guided by the Heisenberg’s value.

But, it will be noticeable and of significance only for small particles like an electron with very low mass. A bigger particle with heavy mass will show the error to be very small and negligible.

Heisenberg Uncertainty Principle Equations
Heisenberg’s uncertainty principle can be considered as a very precise mathematical statement that describes the nature of quantum systems. As such, we often consider two common equations related to the uncertainty principle. They are;

Equation 1: ∆X ⋅ ∆p ~ ħ

Equation 2:  ∆E ⋅ ∆t ~ ħ

Where,

ħ = value of the Planck’s constant divided by 2*pi
∆X = uncertainty in the position
∆p = uncertainty in momentum
∆E = uncertainty in the energy
∆t = uncertainty in time measurement

Heisenberg Uncertainty Principle Problems With Solutions
1. If the position of the electron is measured within an accuracy of + 0.002 nm, calculate the uncertainty in the momentum of the electron. Suppose the momentum of the electron is h / 4pm × 0.05 nm, is there any problem in defining this value.

a) ∆x = 2×10-12m; ∆X  ×  ∆mV  ≥  \frac{h}{4\pi } 
h
  = \frac{6.626\times {{10}^{-34}}}{4\times 3.14} 
4×3.14
6.626×10 
−34
 
 

⸪    ∆mV  ≥   \frac{h}{4\pi \Delta x} 
4πΔx
h
  ≥ \frac{6.626\times {{10}^{-34}}}{4\times 3.14\times 2\times {{10}^{-12}}}\, 
4×3.14×2×10 
−12
 
6.626×10 
−34
 
  = 2.64 × 10-23 Kg m s-1

b) Momentum mv = \,\frac{h\times 5\times {{10}^{-11}}}{4\times {{10}^{-12}}}=\frac{6.626\times {{10}^{-34}}\times 5\times {{10}^{-11}}}{4\times {{10}^{-12}}}\,\, 
4×10 
−12
 
h×5×10 
−11
 
 = 
4×10 
−12
 
6.626×10 
−34
 ×5×10 
−11
 
  = 28 × 10-33

Error in momentum measurement is 1010 times larger than the actual momentum. The given momentum will not be acceptable.

2. Position of a chloride ion on a material can be determined to a maximum error of 1μm. If the mass of the chloride ion is 5.86 × 10-26Kg, what will be the error in its velocity measurement?

∆x =  10-6 m; ∆X  ×  ∆mV  ≥ \frac{h}{4\pi } 
h
  = \,\frac{6.626\times {{10}^{-34}}}{4\times 3.14} 
4×3.14
6.626×10 
−34
 
    = 5.28×10-35Js

⸪    ∆V ≥ \,\frac{h}{4\pi m\Delta x}\ge \frac{6.626\times {{10}^{-34}}}{4\times 3.14\times 5.86\times {{10}^{-26}}\times {{10}^{-6}}}\, 
4πmΔx
h
 ≥ 
4×3.14×5.86×10 
−26
 ×10 
−6
 
6.626×10 
−34
 
  = 9  × 10-4m s-1

3. The lifetime of an excited state of an atom is 3 × 10-3s. What is the minimum uncertainty in its energy in eV?

Time and energy are conjugate pairs with Js unit. The product of measurement error is given by Heisenberg’s principle.

∆t  ×  ∆E  ≥   \frac{h}{4\pi } 
h
  =   \,\frac{6.626\times {{10}^{-34}}}{4\times 3.14} 
4×3.14
6.626×10 
−34
 
  = 5.28×10-35Js

Assuming a maximum error in the measurement of lifetime equal to that of lifetime = 3 ×10-3s

∆E  ≥   \,\frac{h}{4\pi m\Delta x}=\frac{1}{3\times {{10}^{-3}}}\,\, 
4πmΔx
h
 = 
3×10 
−3
 
1
   × 5.28×10-35J

⸪ 1 Joule = 6.242 × 1018ev,

Uncertainty in the determination of energy of the atom = ∆E = 6.22 × 1018 ×  \frac{1}{3\times {{10}^{-3}}}\, 
3×10 
−3
 
1
  × 5.28 ×10-35

= 1.1×10-13

Finding funds: On COP28 and the ‘loss and damage’ fund....

A healthy loss and damage (L&D) fund, a three-decade-old demand, is a fundamental expression of climate justice. The L&D fund is a c...