## Question

A lamp is placed 30 cm above a metal surface which contains atoms of diameter 20 x 10^{-10} m. The lamp can be considered as a point source with power 0.015 W. It may be assumed that each electron can collect energy from a circular area which has a radius equal to that of the atom

a i) Find the intensity of the electromagnetic radiation directed on the atom.

ii) Hence, calculate the power incident on each atom.

iii) Determine, on the basis of wave theory, the time required for an electron to collect sufficient energy to be emitted from the metal if the work function of the metal is 3.2 x 10^{-19} J

iv) Comment on this calculation with actual experimental data and conclude the validity of wave theory.

## Answer

a i) If we treat the lamp as a point source that emits light in all directions (3D),

*Note that the area used is the total area which the power of the lamp is spread over.*

aii) Now that we know the intensity of the light incident on the atom, we can calculate the power incident on the atom.

*Note that the area used is the area of the atom which absorbs the power.*

a iii) Since the electron requires a certain amount of energy to be emitted, we can calculate the time needed.

a iv) This calculation shows that if light were to be treated as a wave, the electron will required 7.68s to collect enough energy to be emitted. However, the experimental data shows that electrons will be emitted almost immediately, with a time much less than 7.68s.

This means that the wave theory cannot be used to describe the photoelectric effect.