Question

The maximum kinetic energy of the photoelectrons varies.

Hint:

The kinetic energy of photoelectrons depends on the wavelength of light, with shorter wavelengths producing higher energy photoelectrons.

Answer 1

Step 1: Relation between kinetic energy and frequency
The photoelectric equation is given by: \[ K.E = h \nu - \phi \] where \( h \) is Planck's constant, \( \nu \) is the frequency of incident light, and \( \phi \) is the work function of the material. Step 2: Frequency and wavelength relation
The frequency \( \nu \) is related to the wavelength \( \lambda \) by: \[ \nu = \frac{c}{\lambda} \] where \( c \) is the speed of light. Step 3: Substituting in the equation
Substituting \( \nu = \frac{c}{\lambda} \) into the photoelectric equation: \[ K.E = \frac{hc}{\lambda} - \phi \] Thus, the maximum kinetic energy of the photoelectrons is inversely proportional to the wavelength \( \lambda \).