Suppose the energy levels of an atom are: - n = 1: E1 = -13.4 eV - n = 2: E2 = -

Question

Suppose the energy levels of an atom are:

- n = 1: E1 = -13.4 eV
- n = 2: E2 = -4.6 eV
- n = 3: E3 = -1.07 eV

a) Find the frequency of the photon emitted when an electron cascades from n = 3 to n = 2.
_________Hz

b) Find the wavelength of the photon emitted when an electron cascades from n = 3 to n = 2.
____________m

c) Find the frequency of the photon emitted when an electron cascades from n = 3 to n = 1.
___________Hz

d) Find the wavelength of the photon emitted when an electron cascades from n = 3 to n = 1.
__________m

e) Find the frequency of the photon emitted when an electron cascades from n = 2 to n = 1.
_________Hz

f) Find the wavelength of the photon emitted when an electron cascades from n = 1 to n = 1.
_________m

g) Suppose an atom has five (5) possible energy states. How many possible photons could this atom emit when the electron cascades from an excited state to a lower energy level?
___________photons

Explanation / Answer

For part A we will use conservation of energy to find the energy of the photon emitted, and then use that to determine the frequency. Remember that for conservation of energy we have: E initial = E final Initially the photon is in the n=3 state and finally we have the electron in the n=2 state plus the energy of the emitted photon E3 = E2 + E photon Now fill in what you know from the given energy levels E3 = -1.07 eV E2 = -4.6 eV -1.07 eV = -4.6 eV + E photon 3.53 eV = E photon Now remember that for a photon E = hf , E=energy, h=planks constant (6.626E-34 Js or using more convenient units in this case, 4.136E-15 eV s), and f = frequency. So solving for frequency we get: f = E/h f = 3.53 eV / (4.136E-15 eV s) f = 8.5348 E14 s -1 = 8.5348 E14 Hz Now remember that for a photon E = hc/lambda where lambda is the wavelength so solving for lambda we get. Lambda = h c / E Lambda = (4.136E-15 eV s) (3.00E8 m/s) / 3.53 eV Lambda = 3.515 E -7 m = 351.5 nm You will use an identical method for each of the following problems simply changing the initial values of the energy levels as specified. The answers I got using this method are as follows: a ) 8.53 E 14 Hz b ) 3.51 E -7 m c ) 3.03 E 15 Hz d ) 9.90 E -8 m e ) 2.18 E 15 Hz f ) No photon would be emitted as there was no change in the energy level and as such no change in the energy of the electron. If any photon of any energy were emitted conservation of energy would be violated e ) 10 possible energy transitions are possible and as such 10 possible photons, the possible transitions are as follows 5:4 5:3 5:2 5:1 4:3 4:2 4:1 3:2 3:1 2:1

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