Calculation of Kinetic Energy:
The kinetic energy of a photoelectron can be calculated using the equation:

KE = hc/λ - φ

where KE is the kinetic energy of the photoelectron, h is Planck's constant (6.626 x 10^-34 J.s), c is the speed of light (3 x 10^8 m/s), λ is the wavelength of the light, and φ is the work function of the metal (the minimum energy required to remove an electron from the metal surface).

Given that the wavelength of the light is 2000 Å (1 Å = 10^-10 m), we can convert it to meters:

λ = 2000 x 10^-10 m = 2 x 10^-7 m

Substituting the values into the equation:

KE = (6.626 x 10^-34 J.s x 3 x 10^8 m/s) / (2 x 10^-7 m) - φ

Simplifying the equation:

KE = (19.878 x 10^-26 J.m) / (2 x 10^-7 m) - φ

KE = 9.939 x 10^-19 J - φ

Given that the range of kinetic energy is from 0 to 3.2 x 10^-19 J, we can set up an equation to find the work function:

0 ≤ 9.939 x 10^-19 J - φ ≤ 3.2 x 10^-19 J

Solving for φ:

-3.2 x 10^-19 J ≤ -φ ≤ -9.939 x 10^-19 J

Taking the absolute value of both sides:

3.2 x 10^-19 J ≥ φ ≥ 9.939 x 10^-19 J

Calculation of Stopping Potential:
The stopping potential (V) is the voltage required to stop the photoelectrons from reaching the collector plate. It can be calculated using the equation:

V = KE/e

where V is the stopping potential, KE is the kinetic energy of the photoelectron, and e is the elementary charge (1.602 x 10^-19 C).

Substituting the value of KE into the equation:

V = (9.939 x 10^-19 J - φ) / (1.602 x 10^-19 C)

Since the work function (φ) falls within the range of 9.939 x 10^-19 J to 3.2 x 10^-19 J, we can substitute the upper and lower limits of φ into the equation to find the maximum and minimum values of the stopping potential.

For φ = 9.939 x 10^-19 J:

V = (9.939 x 10^-19 J - 9.939 x 10^-19 J) / (1.602 x 10^-19 C) = 0 V

For φ = 3.2 x 10^-19 J:

V = (9.939 x 10^-19 J - 3.2 x 10^-19 J) / (1.602 x 10^-19 C) ≈ 3.11 V

Therefore, the stopping potential will be between 0 V and 3.11 V.

Dharaniya