Question

In a series of experiments, a gas of exotic molecules containing exactly one electron

each is investigated. It is found that:

• When the gas is cold (so all the molecules are in their ground states) and illuminated

with light, it absorbs strongly at wavelengths 103.40nm, 137.87nm and 248.16nm.

• When the gas is cold and illuminated with light of short wavelength, the electrons are

ejected from the molecules as long as the wavelengths is less than 88.63nm.

• When the gas is heated, it emits light with 6 different wavelengths.

(a) If we chose to set the potential energy outside of the molecule to be zero, how far

below zero energy is the ground state of the molecule?

(b) How many discrete energy level does the molecule have?

(c) What wavelengths of light does the heated gas emit?

(d) A free electron with kinetic energy of 2eV is captured by the atom (which is originally ionized) and goes directly into the ground state. What is the wavelength of the emitted photon?

Hint: Electrons can jump from one energy level to another by emitting/absorbing a photon whose energy is equal to the difference in energies between the two states.

Answer 1

energy of photon E = hc/

hc = 1240 ev-nm

energy pf the photons absorbed by the molecules

88.63 nm : E = 1240/88.63 = 13.991 ev , electron is knocked out

103.4 nm : E = 1240/103.4 = 11.992 ev

137.87nm -> E = 8.994 ev

248.16 nm ---> E = 4.997 ev

a) 88.63 nm wave length knock out the electron from the molecule. Its ionisation potential is 13.991 ev

considering the outside potential as 0, the molecule ground state is at -13.991 eV

b) The molecule has 3 discrete energy levels 4.997 ev, 8.994 ev and 11.992 ev

c) When gas is heated the molecule is ionised and comes back to ground state directly or through different levels and during the process emits the difference of energy between different levels. They are

direct ground state -> 88.63 nm

E3 -> E0 = 103.4 nm

E2 -> E0 = 137.87 nm

E1 --> E0 = 248.16 nm

E3 ---> E2 = 3 ev = 413.33 nm

E2 ---> E1 = 4ev = 310 nm

d) When the molecule is ionised it ia 13.99 ev above its ground state. The electron has a KE of 2ev. The electron goes to the E3 level orbit and then the molecule goes to ground state. Photon emitted is equal to the energy difference from E₃ level

wave length = 103.4 nm