Part A In the Bohr model of the hydrogen atom, what is the de Broglie wavelength

Question

Part A

In the Bohr model of the hydrogen atom, what is the de Broglie wavelength for the electron when it is in the n = 3 level?

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Part B

In the Bohr model of the hydrogen atom, what is the de Broglie wavelength for the electron when it is in the m = 6 level?

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Part C

Compare the de Broglie wavelength to the circumference 2?r3 of the orbit in part A.

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Part D

Compare the de Broglie wavelength to the circumference 2?r6 of the orbit in part B.

Explanation / Answer

FOR PART A,PART B  de Broglie wavelength is

In this case the radius is the Bohr radius.
L = mvr = nh/(2*pi) (correct)
P = mv = h/?
Substitute:
(h/?)*r = n*h/(2*pi) where n=1
2*pi*r = n? ==> de Broglie wavelength

Now, the Bohr radius is about r = 5.29 * 10^-11 m
Hence, in the simple Bohr model, the number de Broglie wavelengths
that "fit" depend on the discrete radii of the orbits. The radii can be
derived from other constants and equations.

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