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A mono-chromatic point source S radiating wavelength \mathrm{6000 \AA} with power 2 \mathrm{w}_1 an aperture A of diameter 0.1 metre and a large screen Sc are placed as shown in figure. A photo emission detector D of surface Area 0.5 \mathrm{~cm}^2 is placed at the centre of the screen. The efficiency of the detector for the photo-electro generation per incident photon is 0.9

Question:

A small plate of a metal (work function = 1.17 eV) is placed at a distance of 2 m from a monochromatic light sourceof wavelength 4.8 \times 10^{-7} \mathrm{~m} and power 1.0 watt. The light falls normally on the plate. Find the number of photons striking the metal plate per square metre per second.

Option: 1

1.55 eV


Option: 2

1.45 eV


Option: 3

1.40 eV


Option: 4

1.30 eV


Answers (1)

best_answer

\mathrm{\text { Photon energy }=\frac{h c}{\lambda}=\frac{\left(6.6 \times 10^{-34}\right) \times\left(3 \times 10^8\right)}{4.8 \times 10^{-7}}=4.125 \times 10^{-19} \text { joule }}

The rate of emission of photon from source

\mathrm{=\frac{1.0 \text { joule } / \text { sec } .}{4.125 \times 10^{-19} \text { joule }}=2.424 \times 10^{18} \text { per sec. }}

Number of photons striking per sq. metre per second on the plate

\mathrm{\frac{2.425 \times 10^{18}}{4 \times(3.14) \times(2)^2}=4.82 \times 10^{16}}

The maximum kinetic energy of the photo-electrons emitted from the plate having work function W = 1.17 eV is given by

\mathrm{\begin{aligned} & E_k=\frac{h c}{\lambda}-W \\ & =\left(4.125 \times 10^{19} \text { joule }\right)-\left(1.17 \times 1.6 \times 10^{19} \text { joule }\right) \\ & =2.253 \times 10^{-19} \text { joule }=1.40 \mathrm{eV} \end{aligned}}

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Rishabh

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