a) According to the Bohr model of the hydrogen atom, energy levels are given as

Question

a) According to the Bohr model of the hydrogen atom, energy levels are given as En= -13.6 eV/n2 . Determine hydrogen’s first four energy levels.
n=4, E = ___________
n=3, E = ___________
n=2, E = ___________
n=1, E = ___________

b) Based on your energy level calculations, predict the photon energies that would be emitted by transitions between the hydrogen energy levels.

c) Which of the photon energies are in the energy range of visible spectrum (400 nm to 700 nm)? h=4.1×10-15 eV·s; speed of light: c=3×108 m/s

d) If photon emitted in transition n=3 to n=1 will eject photoelectrons from an unknown metal, but photon emitted in the transition n=4 to n=2 cannot, what are the limits of the threshold frequency (fo) of the metal?

Explanation / Answer

a) E4 = -13.6/4^2 = -0.85 eV

E3 = -13.6/3^2 = -1.51 eV

E2= -13.6/2^2 = -3.4 eV

E1 = -13.6/1 = -13.6 eV

b) E21 = -3.4+13.6 = 10.2 eV

E31 = 13.6-1.51 = 12.09 eV

E41= 13.6-0.85 = 12.75 eV

E32 = 3.4-1.51 = 1.89 eV

E42= 3.4-0.85 = 2.55 eV

E43 = 1.51-0.85 = 0.66 eV

c) minimum energy = hc/lambda = 4.1e-15*3e8/700e-9 = 1.757 eV

  maximum energy = hc/lambda = 4.1e-15*3e8/400e-9 = 3.075 eV

only two transitions, E32, E42 will lie in visible spectrum

d) 2.55eV < work function of metal < 12.09 eV

lower limit threshold frequency = 2.55 eV/(4.1e-15eV s) = 6.22*10^14 Hz

upper limit threshold frequency = 12.09 eV/(4.1e-15eV s) = 2.95*10^15 Hz

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