6. The orange-yellow color of sodium-vapor streetlights results from electrons i

Question

6. The orange-yellow color of sodium-vapor streetlights results from electrons in sodium atoms falling from 3p to 3s orbitals. The wavelength of one of these orange-yellow lines in the spectrum of sodium is 589.0 nm. a. What is the frequency of the photon responsible for this emission line? b. What is the energy of the photon of light at this wavelength? c. Calculate the difference in energy between the 3 p and 3 s orbitals of the sodium atom. d. Write every set of quantum numbers associated with the electrons in the ground state of sodium. e. Write the electron configuration for the ground state of sodium. f. Write the electron configuration of the excited state of the sodium atom that is involved in this change in energy level g. Determine the number of unpaired electrons in the excited state of sodium. Draw an orbital diagram to illustrate the paired and unpaired electrons.

Explanation / Answer

a)

Relate frequency, v with wavleneght WL as follows

WL = c/v

v = c/WL

v = (3*10^8)/(589*10^-9) =5.0933*10^14 Hz

b)

E = hv

then

h = Planck Constant = 6.626*10^-34 J s

c = speed of particle (i.e. light) = 3*10^8 m/s

E = energy per particle J/photon

E = (6.626*10^-34)(5.0933*10^14) =3.374*10^-19 J/photon

c)

difference in energy

dE = Ereleased = 3.374*10^-19 J/photon

d)

we required at least

n = level, which is 3

l = orbital, 0 for s, and 1 for p

ml = orientaiton, assume "x" so ml = 0

ms = spin, assume 1/2

(3,1,0,+1/2) to --> (3,2,0,+1/2)

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