When the wavelength of radiation falling on a metal

Question:

When the wavelength of radiation falling on a metal is changed from $500 \mathrm{~nm}$ to $200 \mathrm{~nm}$, the maximum kinetic energy of the photoelectrons becomes three times larger. The work function of the metal is close to :

  1. $0.61 \mathrm{eV}$

  2. $0.52 \mathrm{eV}$

  3.  $0.81 \mathrm{eV}$

  4. $1.02 \mathrm{eV}$


Correct Option: 1

Solution:

$\frac{3}{1}=\frac{\frac{h c}{200 \mathrm{~nm}}-\phi}{\frac{h c}{500 \mathrm{~nm}}-\phi}, h c=1240 \mathrm{eV}-\mathrm{nm}$

On solving $\phi=0.61 \mathrm{eV}$

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