1. [15] According to the classical picture of the hydrogen atom, a single electr
ID: 1954540 • Letter: 1
Question
1. [15] According to the classical picture of the hydrogen atom, a single electron orbits a proton in a circular orbit at a distance equal to the Bohr radius (see Appendix D in your textbook).a. [5]Use Coulomb’s force and centripetal acceleration to calculate the speed of the electron (ignore any relativistic effects) in metres per second and as a fraction of the speed of light,vcß=.
b. [3] Determine the frequency (in Hz) and wavelength (in nm) of the light emitted by this electron. NOTE that classically the frequency of the emitted light should equal to the frequency of the orbital motion of the electron.
c. [1] To what part of the electromagnetic spectrum does this frequency belong?
d. [1] Does this frequency correspond to any of the spectral lines in the Hydrogen atom? Search the internet for hydrogen spectrum and provide a link that supports your answer.
Explanation / Answer
a) Gravitational force is
F = [G mpme] / r2
Centripetal force is
F = mev2 / r
We know to use the mass of the electron here, since the force is acting on it (and not on the proton)
Set the equations equal to each other, and cancel out the electron's mass and one r
V2 = (Gmp)/ r
where G is 6.67 x 10-11 , and r and the mass are givens.
Solve for V. Fractions is V/C
b) f = 1/T
Since the frequency of the light is equal to the orbital frequency, we can use the above equation. We now need to find the time in which the electron makes one revolution. Using the given radius, find the cirumference (C = 2r), and using the equation
t = d/v
find the time, where v is the velocity from part a) and d is the circumference.
Also,
f = v /
so
= v / f
Using the velocity from a) and the frequency just found, find the wavelength.
c) Reference the textbook
d) Use references
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