CUET Preparation Today
A photoelectric surface is illuminated successively by monochromatic light of wavelength 2λ and 0.5λ. What will be the work function of the photosensitive material of the maximum kinetic energy of the photo electrons in the second case is 5 times that of the first case? In the given options h is Plank's constant and c is the speed of light. |
$\frac{4hc}{λ}$ $\frac{5hc}{λ}$ $\frac{4hc}{3λ}$ $\frac{hc}{8λ}$ |
$\frac{hc}{8λ}$ |
| {Let the Einstein's photoelectric equation be:} \[ K_{{max}} = \frac{hc}{\lambda} - \phi \] where: - \( K_{{max}} \) = maximum kinetic energy of emitted photoelectrons - \( h \) = Planck’s constant - \( c \) = speed of light - \( \lambda \) = wavelength of incident light - \( \phi \) = work function of the material {For the first case (wavelength = \( 2\lambda \)):} \[ K_1 = \frac{hc}{2\lambda} - \phi \] {For the second case (wavelength = \( 0.5\lambda \)):} \[ K_2 = \frac{hc}{0.5\lambda} - \phi = \frac{2hc}{\lambda} - \phi \] {Given that:} \[ K_2 = 5K_1 \] {Substitute \( K_1 \) and \( K_2 \):} \[ \frac{2hc}{\lambda} - \phi = 5\left( \frac{hc}{2\lambda} - \phi \right) \] {Simplify the equation:} \[ \frac{2hc}{\lambda} - \phi = \frac{5hc}{2\lambda} - 5\phi \] \[ {Multiply through by 2:} \] \[ \frac{4hc}{\lambda} - 2\phi = \frac{5hc}{\lambda} - 10\phi \] {Rearranging terms:} \[ -2\phi + 10\phi = \frac{5hc}{\lambda} - \frac{4hc}{\lambda} \] \[ 8\phi = \frac{hc}{\lambda} \] {Solving for \( \phi \):} \[ \phi = \frac{hc}{8\lambda} \] |
