1. Tardigrade
  2. Question
  3. Physics
  4. A photosensitive metallic surface has work function, h v0. If photons of energy 2 h v0 fall on this surface, the electrons come out with a maximum velocity of 4 × 106 m / s. When the photon energy is increased to 5 h v0, then maximum velocity of photoelectrons will be

Question Error Report

Thank you for reporting, we will resolve it shortly

Back to Question

Q. A photosensitive metallic surface has work function, $h v_{0}$. If photons of energy $2 h v_{0}$ fall on this surface, the electrons come out with a maximum velocity of $4 \times 10^{6}\, m / s$. When the photon energy is increased to $5 \,h v_{0}$, then maximum velocity of photoelectrons will be

JIPMERJIPMER 2007Dual Nature of Radiation and Matter

Solution:

The solution to our problem consists, in Einsteins photoelectric equation.
Einsteins photoelectric equation can be written as
$\frac{1}{2} m v^{2}=h v-\phi $
$\Rightarrow \frac{1}{2} m \times\left(4 \times 10^{6}\right)^{2}=2 h v_{0}-h v_{0}\,\,\,\,...(i)$
and $\frac{1}{2} m \times v^{2}=5 h v_{0}-h v_{0}\,\,\,\,....(ii)$
Dividing Eq. (ii) by (i), we get
$\frac{v^{2}}{\left(4 \times 10^{6}\right)^{2}}=\frac{4 h v_{0}}{h v_{0}}$
$\Rightarrow v^{2}=4 \times 16 \times 10^{12} $
$\Rightarrow v^{2}=64 \times 10^{12} $
$\therefore v=8 \times 10^{6}\, m / s$
NOTE: The efficiency of photoelectric effect is less than $1 \%$ i.e., number of photons less than $1 \%$ are capable of ejecting photoelectrons.