Consider a Bohr model of doubly ionized lithium. (a) Write an expression similar

Question

Consider a Bohr model of doubly ionized lithium.
(a) Write an expression similar to En = -13.6 eV/n2 ? E2 = -13.6 eV/22 = -3.40 eV for the energy levels of the sole remaining electron. (Use the following as necessary: n.)
(b) Find the energy corresponding to n = 8.
(c) Find the energy corresponding to n = 1.
(d) Calculate the energy of the photon emitted when the electron transits from the eighth energy level to the first energy level. Express the answer both in electron volts and in joules.
(e) Find the frequency and wavelength of the emitted photon.

Explanation / Answer

a)  En = -(13.6 x z2 )/ n2  eV

         = -(13.6 x 9 ) /  n2  eV   = 122.4 / n2  eV

b) E8  =  122.4 / 82  eV   = 1.92 eV

c) E1 = 122.4 eV

d) Change in E = 122.4 -1.92 = 120.48 eV = 1.93 x 10-17  J

e)  E = hf

f = 2.9 x 1017 Hz

= c/f = 1.03 x 10 -9  m  = 1.03 nm

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