A point source of monochromatic light of `1.0 mW` is placed at a distance of `5.0 m` from a metal surface. Light falls perpendicularly on the surface. Assume wave theory of light to hold and also that all the light falling on the circular area with radius `=1.0 xx 10^-9m`(which is few times the diameter of an atom) is absorbed by a single electron on the surface. Calculate the time required by the electron to receive sufficient energy to come out of the metal if the work function of the metal is `2.0eV`.

Explanation

To solve the problem, we need to calculate the time required for an electron to receive enough energy to escape from a metal surface when illuminated by a monochromatic light source. Here's a step-by-step breakdown of the solution:

### Step 1: Understand the Given Data
- Power of the light source, \( P = 1.0 \, \text{mW} = 1.0 \times 10^{-3} \, \text{W} \)
- Distance from the light source to the metal surface, \( d = 5.0 \, \text{m} \)
- Radius of the circular area, \( r = 1.0 \times 10^{-9} \, \text{m} \)
- Work function of the metal, \( \phi = 2.0 \, \text{eV} = 2.0 \times 1.6 \times 10^{-19} \, \text{J} = 3.2 \times 10^{-19} \, \text{J} \)

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