If p is the momentum of the fastest electron ejected from a metal surface after the irradiation of light having wavelength ` lamda`, then for 1.5 p momentum of the photoelectron, the wavelength of the light should be ` ( 4 ) /(a) lamda`. What is numerical value of a ? (Assume kinetic energy of ejected photoelectron to be very high in comparison to work function):

Explanation

To solve the problem, we need to analyze the relationship between the momentum of the photoelectron and the wavelength of the light used to eject it from the metal surface.

### Step-by-Step Solution:

1. **Understanding Momentum and Kinetic Energy**:
- The momentum \( p \) of the fastest electron ejected can be expressed as:
\[
p = mv
...