A 10 watt source produces monochromatic light with a 3000 nm wavelength. It releases photoelectrons from a photosensitive metallic surface when positioned 1 meters away. What will be the number of emitted photons if the source is placed 0.5 m away from the detector?

Increased by the factor of 4

The number of photoelectrons emitted per second is directly proportional to the intensity of the incident radiation, which can be varied by changing the distance between the source and detector.

The intensity of light ∝ 1/(distance)² 

d = 1 m

d' = 0.5 m = d/2 

I = 1/(d/2)² = 4/d² 

So if d becomes half, number of electrons emitted (intensity) will increase by the factor of four.