Help With Heisenberg's Energy-Time Uncertainty Principle

In summary, the conversation discusses the use of Heisenberg's energy-time uncertainty principle to calculate ΔE. The individual is getting an incorrect answer of 0.743e-33 eV when using a time conversion of 1.4e10 years to seconds. They question where they may have made a mistake and suggest using a different conversion factor. The conversation also mentions the uncertainty involved in these calculations and provides a mnemonic for quick estimations.
  • #1
tanaygupta2000
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14
Homework Statement
What is the maximum theoretical accuracy ΔE to which an ideal experiment may
determine the energy levels of the hydrogen atom? (Hint: Use the fact that the age of the universe is estimated to be approximately 1.4e10 years)
Options:
(a) 4.7e-26 eV
(b) 9.4e-33 eV
(c) 1.2e-63 eV
(d) 2.4e-70 eV
Relevant Equations
ΔEΔt = ћ/2
So according to Heisenberg's energy-time uncertainty principle, the product of accuracies in energy and time is equal to ћ/2.
In this problem, I know I have to calculate ΔE. But when I'm using Δt = 1.4e10 yrs. = 4.41e17 s, I am getting ΔE = 0.743e-33 eV, which is certainly incorrect!
Where am I doing mistake? Please help!
 
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  • #2
This question basically asks you to put some meaningless numbers into a calculator and get a meaningless number out. And you've got a meaningless number not on the list?

You must have pressed the wrong buttons on you calculator, I guess.
 
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  • #3
tanaygupta2000 said:
I'm using Δt = 1.4e10 yrs. = 4.41e17 s
That part at least would look to be incorrect. I get the 4.41 part but a different exponent... (and actually 4.42 since there are 365.25 days/year)
 
  • #4
Just for the sake of playing with my calculator, I used h instead of hbar/2. With this choice, I found answer (b)
 
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  • #5
Gordianus said:
Just for the sake of playing with my calculator, I used h instead of hbar/2. With this choice, I found answer (b)
Um, how about the earlier time units conversion? Did you use his number or your own?
 
  • #6
1.4e10 years*(365.25 days/year)*(86400 seconds/day)
 
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  • #7
tanaygupta2000 said:
I am getting ΔE = 0.743e-33 eV, which is certainly incorrect!
How can you be so certain when the Uncertainty Principle is involved? The UP is only an order of magnitude estimate. As far as order of magnitude is concerned, answer (b) is spot on.
 
Last edited:
  • #8
Gordianus said:
π×1.4e10 years*(365.25 days/year)*(86400 seconds/day)
A decent mnemonic for back-of-the-envelope calculations is 1 year = π × 107 s. It is an underestimate by about 1.7 days.
 

FAQ: Help With Heisenberg's Energy-Time Uncertainty Principle

What is Heisenberg's Energy-Time Uncertainty Principle?

Heisenberg's Energy-Time Uncertainty Principle is a fundamental principle in quantum mechanics that states that it is impossible to know both the energy and the time of a quantum system with absolute certainty. This means that the more precisely we know the energy of a particle, the less precisely we can know its time, and vice versa.

How does Heisenberg's Energy-Time Uncertainty Principle relate to other uncertainty principles?

Heisenberg's Energy-Time Uncertainty Principle is similar to other uncertainty principles, such as the Heisenberg Uncertainty Principle which relates to the position and momentum of a particle. However, the energy and time uncertainty principle is unique in that it is a result of the fundamental properties of quantum systems, rather than limitations of measurement.

Why is Heisenberg's Energy-Time Uncertainty Principle important?

Heisenberg's Energy-Time Uncertainty Principle is important because it sets a limit on the precision with which we can measure certain properties of quantum systems. This has significant implications in fields such as quantum mechanics, where precise measurements are crucial for understanding the behavior of particles at the subatomic level.

How does Heisenberg's Energy-Time Uncertainty Principle affect our understanding of the universe?

Heisenberg's Energy-Time Uncertainty Principle challenges our traditional understanding of causality and determinism. It suggests that at the quantum level, events are not always predictable and that there is a fundamental limit to the precision with which we can measure certain properties. This principle has also led to the development of new theories and concepts, such as the concept of quantum entanglement.

Can Heisenberg's Energy-Time Uncertainty Principle be violated?

No, Heisenberg's Energy-Time Uncertainty Principle is a fundamental principle in quantum mechanics and has been extensively tested and confirmed by experiments. It is not possible to violate this principle, but it can be used to make predictions and calculations about the behavior of quantum systems.

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