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## GR0877 Problem 27

PROBLEM STATEMENT: This problem is still being typed.

SOLUTION: (C) Use the energy-time uncertainty principle: $\Delta E \Delta t \gtrsim h/(2\pi)$. Rewriting $\Delta E$ as $h \Delta \nu$, one has $\displaystyle \Delta \nu \sim \frac{1}{2\pi \Delta t} = \frac{1}{2 \pi \tau} = (2 \cdot 3.14 \cdot 1.6 \cdot 10^{-9})^{-1} \text{~Hz} \approx 100 \text{~MHz}$, as in choice (C).

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1. 09.11.2011 at 03:06

I believe the uncertainty principle constant is actually h-bar/2. That would introduce a factor of pi in the denominator of your final calculation and get your answer close to 200 MHz

2. 09.11.2011 at 03:11

Oops, that would introduce a factor of 4pi, actually, and you’d get something like 50MHz. But it seems that some people say deltaEdeltaT is hbar, some say h, some say hbar/2. I suppose they’re all approximations anyway, and any of them get you in the ballpark to answer this question….

3. 06.09.2016 at 05:02

Why is this an application of the energy-time uncertainty principle?