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Photoelectric Effect and WaveParticle Duality — Physics STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 SciencePhysicsPhotoelectric Effect and WaveParticle Duality5 Marks
Question
The work function of a photoelectric material is 4.0eV.
  1. What is the threshold wavelength?
  2. Find the wavelength of light for which the stopping potential is 2.5V.
✓

Answer

$\phi=4\text{ev}=4\times1.6\times10^{-19}\text{J}$
  1. Threshold wavelength $=\lambda$
$\phi=\frac{\text{hc}}{\lambda}$

$\Rightarrow\lambda=\frac{\text{hc}}{\phi}=\frac{6.63\times10^{-13}\times3\times10^8}{4\times1.6\times10^{-19}}$

$=\frac{6.63\times2}{6.4}\times\frac{10^{-27}}{10^{-9}}=3.1\times10^{-7}\text{m}=310\text{nm}.$
  1. Stopping potential is 2.5V
$\text{E}=\phi+\text{eV}$

$\Rightarrow\frac{\text{hc}}{\lambda}=4\times1.6\times10^{-19}+1.6\times10^{-19}\times2.5$

$\Rightarrow\lambda=\frac{6.63\times10^{-34}\times3\times10^8}{\lambda\times1.6\times10^{-19}}=4+2.5$

$\Rightarrow\frac{6.63\times10^{-34}\times3\times10^8}{\lambda\times1.6\times10^{-19}\times6.5}=1.9125\times10^{-7}=190\text{nm.}$

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