A photon of wavelength 3315 Ã… falls on a photocathode and an electron of energy $3 \times 10^{-19}…

A photon of wavelength 3315 Ã… falls on a photocathode and an electron of energy $3 \times 10^{-19} \mathrm{~J}$ is ejected. The threshold wavelength of photon is [Planck's constant (h) $=6.63 \times 10^{-34} \mathrm{~J}-\mathrm{s}$, velocity of light $\left.(\mathrm{c})=3 \times 10^{8} \mathrm{~m} / \mathrm{s}\right]$
  1. $6630 Å$
  2. $3315 Å$
  3. $5000 Å$
  4. $1130 Å$

Solution

$\phi_{0}=\frac{h c}{\lambda}-E$ $=\frac{6.63 \times 10^{-34} \times 3 \times 10^{8}}{3315 \times 10^{-10}}-3 \times 10^{-19}=(6-3) \times 10^{-19}=3 \times 10^{-19}$ $\lambda_{0}=\frac{\mathrm{hc}}{\phi_{0}}=\frac{6.63 \times 10^{-34} \times 3 \times 10^{8}}{3 \times 10^{-19}} \approx 6630 ~Å$

Asked in: MHT CET 2020 (20 Oct Shift 1)

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