Question

Modern Physics: Experimental basis for quantum theory + Atomic models

Use the value for the intensity of sunlight at the surface of the earth from the previous question. Assume that all the light has the same frequency, 5 x 10^14? Hz.

a. Classical approximation: if the light described above is incident upon a 1 m²? patch of sodium metal, calculate the average amount of energy each atom in the surface
   receives per second as well as the amount of time it would take an electron, on average, to gain enough energy to overcome the work function.
Hint - there will be? approximately 1019 sodium atoms in the surface layer and the work function of sodium is 2.3 eV.

b. Determine the number of photons per second on the patch of sodium metal and their energy. Would photons from sunlight be energetic enough to eject photoelectrons
from the metal?

Answer 1

a)

Let's assume the intensity of sunlight is 1370 W/m^2.

Since the area of patch of sodium metal is 1 m^2.

Therefore, the power received per second will be 1370 W or 1370 J/s.

Since, the number of atoms on the surface is 10^19.

Therefore, average amount of energy received by an atom will be 1370/10^19 J/s =J/s=

Assuming all the energy received by an atom is transferred to the electron present in valance cell.

Then the amount of time , on average it will require to gain enough energy to overcome the work function will be

b) Energy of photon will be

E=hf=

Also the number of photons per second on the patch will be

Since, the energy of a photon is less than that of the work function so a photon is not energetic enough to eject photoelectrons from the metal.