1. Tardigrade
  2. Question
  3. Physics
  4. A small metal plate (work function =1.17 eV ) is placed at a distance of 2 m from a monochromatic light source of wavelength 4.8 × 10-7 m and power 20 watt. The light falls normally on the plate. The number of photons striking the metal plate per second per sq metre area will be

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Q. A small metal plate (work function $=1.17 \,eV$ ) is placed at a distance of $2 \,m$ from a monochromatic light source of wavelength $4.8 \times 10^{-7} m$ and power 20 watt. The light falls normally on the plate. The number of photons striking the metal plate per second per sq metre area will be

Dual Nature of Radiation and Matter

Solution:

Energy of photon emitted $=h c / \lambda$;
the energy of light falling per second per unit area of a metal surface
$=P /\left(4 \pi r^{2}\right)$
$\therefore $ No. of photons falling per second per unit area of metal surface
$=\frac{P}{4 \pi r^{2}} \times \frac{\lambda}{h c}$
$=\frac{20 \times 4.8 \times 10^{-7}}{4 \times 3.14 \times 2^{2} \times 6.6 \times 10^{-34} \times 3 \times 10^{8}}$
$=9.65 \times 10^{17}$