Question

a) Calculate the cut-off wavelength for aluminium, which has a work function of

4.08 eV. Will photo electrons be emitted when radiation of wavelength 400 nm is

incident on an aluminium surface?

(b) Calculate the de Broglie wavelength of a non-relativistic proton with a kinetic

energy of 10 eV.

(c) An excited state in an atom has a life time of Calculate the line 3.0 x10^-7s

width of the emitted photon, when the atom decays spontaneously to its ground

state.

Answer 1

a) The threshold wavelength for observing the photoelectric effect in aluminium is

$$\lambda_c=\frac{hc}{\phi}=\frac{1240}{4.08}=304\ nm$$

The incident radiation has wavelength 400 nm, which is longer than the cut-off wavelength; therefore, photoelectrons are not observed.

b)

$$\lambda=\frac{2\pi hc}{pc}\\ \lambda=\frac{2\pi (197.3)}{\sqrt{2(938\cdot10^6)(10)}}=0.00905\ nm$$

c)

$$\Delta E=\frac{6.63\cdot10^{-34}}{4\pi(3\cdot10^{-7})}=1.8\cdot10^{-28}J$$