Please explain and show formula and work. Answer is given already, thank you. Pl

Question

Please explain and show formula and work. Answer is given already, thank you.

Please explain and show formula and work. Answer is given already, thank you. An electron in an excited hydrogen atom makes two transitions. First the electron drops from the n = 7 to the n = 4 state, then the electron drops from the n = 4 to the n = 1 state. Calculate the frequency of the photon emitted in the first transition. Calculate the momentum of the photon emitted in the second transition. Which of the following quantum states could the electron have been in at some point during these transitions?

Explanation / Answer

1. apply energyE = 13.6*(1/n^2-1/m^2)

E = 13.6*(1/4^2-1/7^2)

E = 0.572 eV   

or 0.572*1.6*10^-19

E = 9.15 *10^-20 J

now apply E = hf

so frequency f = 9.15*10^-20/6.626*10^-34
f = 1.38*10^14 Hz

option A    1.4 *10^14 Hz

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2. apply 1/L = R(1/n^2-1/m^2)

where L = wavelength, R = Rydberg constant = 1.1*10^7

so 1/L = 1.1e7 *(1/1-1/16)

1/L = 1.0315*10^7

L = 96.95 nm

now use L = h/mv

moemntum P = mv = 6.626*10^-34/96.95nm
P = 6.83 *10^-27 kgm/s

option C

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3. option d

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