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11.Dual Nature of Radiation and matter
normal
$10^{-3} \, W$ of $5000\, \mathring A $ light is directed on a photoelectric cell. If the current in the cell is $0.16 \mu A$, the percentage of incident photons which produce photoelectrons, is.......$\%$
A$0.4$
B$.04$
C$20$
D$10$
Solution
$=\frac{\mathrm{n} / \Delta \mathrm{t}}{\mathrm{N} / \Delta \mathrm{t}} \times 100$ $…(1)$
$\because \mathrm{I}=\frac{\mathrm{ne}}{\Delta \mathrm{t}}$
$\frac{\mathrm{n}}{\Delta \mathrm{t}}=\frac{\mathrm{I}}{\mathrm{e}}=\frac{0.16 \times 10^{-16}}{1.6 \times 10^{-19}}$
$\therefore \frac{\mathrm{n}}{\Delta \mathrm{t}}=10^{12}$ $…(2)$
and $\quad \mathrm{W}=\frac{\mathrm{N}}{\Delta \mathrm{t}} \frac{\mathrm{hc}}{\lambda}$
$\therefore \frac{\mathrm{N}}{\Delta \mathrm{t}}=\frac{\mathrm{W} \lambda}{\mathrm{hc}}=\frac{10^{16}}{4}$ $…(3)$
Persentage $=\frac{10^{12}}{10^{16}} \times 4 \times 100$
$[\text { from eq. }(1),(2) \text { and }(3)]$
Persentage $=0.04 \%$
$\because \mathrm{I}=\frac{\mathrm{ne}}{\Delta \mathrm{t}}$
$\frac{\mathrm{n}}{\Delta \mathrm{t}}=\frac{\mathrm{I}}{\mathrm{e}}=\frac{0.16 \times 10^{-16}}{1.6 \times 10^{-19}}$
$\therefore \frac{\mathrm{n}}{\Delta \mathrm{t}}=10^{12}$ $…(2)$
and $\quad \mathrm{W}=\frac{\mathrm{N}}{\Delta \mathrm{t}} \frac{\mathrm{hc}}{\lambda}$
$\therefore \frac{\mathrm{N}}{\Delta \mathrm{t}}=\frac{\mathrm{W} \lambda}{\mathrm{hc}}=\frac{10^{16}}{4}$ $…(3)$
Persentage $=\frac{10^{12}}{10^{16}} \times 4 \times 100$
$[\text { from eq. }(1),(2) \text { and }(3)]$
Persentage $=0.04 \%$
Standard 12
Physics
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