Help With Heisenberg's Energy-Time Uncertainty Principle

[tanaygupta2000]

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!

 

[PeroK]

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.

 

[berkeman]

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)

 

[Gordianus]

Just for the sake of playing with my calculator, I used h instead of hbar/2. With this choice, I found answer (b)

 

[berkeman]

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?

 

[Gordianus]

1.4e10 years*(365.25 days/year)*(86400 seconds/day)

 

[kuruman]

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.

 

[kuruman]

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.