- #1

Summer95

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**A check my work question...**

Homework Statement

Homework Statement

Louis de Broglie tried to explain Bohr’s hydrogen atom electron orbits as being circles of just the

right circumference such that an electron of the Bohr energy going around the circle will

interfere constructively with itself. This seems to give a nice explanation of the angular momentum quantization.

**The attempt at a solution**

Q1: what would be the wavelength of such a wave in the ground state of hydrogen?

## \lambda n=2\pi r## from the Bohr energy equation we can tell n=1 gives the lowest energy state. We also have an equation for the possible values of r which reduces to ##r=a_{0}n^{2}## and so in our case ##\r=a_{0}##. Therefore ## \lambda n=2\pi r## becomes ## \lambda =2\pi a_{0} =0.332nm ##. Where ##a_{0}=0.0529##.

Q2: According to the uncertainty principle, what would be the uncertainty in the wavelength, given that the electron position is known to be somewhere within the atom?

At first I tried to do it using ##\Delta x \Delta p\geq \frac{\hbar}{2}##

but then I found the expression ##\Delta k\Delta x\geq \frac{1}{2} ## in my text and so since uncertainty in position is equal to the radius of the atom (at least approximately) we have ##\Delta k \geq \frac{1}{2r_{atom}}## and therefore I just said the uncertainty in wavelength is just ##2r_{atom}##.

Q3: Does this model make sense? Explain.

Before I go trying to answer the last question and try to explain what I have done and found I'd like a little input on whether I am on the right track so far. Is my thinking correct here?

Thank you so much!