A certain metallic surface is illuminated with monochromatic light of wavelength, \lambda. The stopping potential for photo-electric current for this light is 3V0. If the same surface is illuminated with light of wavelength 2\lambda, the stopping potential is V0. The threshold wavelength for this surface for photo-electric effect is:

  • Option 1)

    4 \lambda

  • Option 2)

    \frac{\lambda}{4}

  • Option 3)

    \frac{\lambda}{6}

  • Option 4)

    6 \lambda

 

Answers (1)

 

Stopping Potential /Cut-off Potential -

It is defined as the potential necessary to stop any electron from reaching the other side.

-

 

 and

Conservation of energy -

h\nu = \phi _{0}+\frac{1}{2}mv^{2}_{max}

h\nu = h\nu _{0}+\frac{1}{2}mv^{2}_{max}

 

h\left ( \nu-\nu _{0} \right )=\frac{1}{2}mv^{2}_{max}

where, h - Plank's constant\ \nu - Frequency\ \nu_{0} - threshold\ frequency\ \phi_{0}- work function

- wherein

 

 1st Case: 3eV_{0}= \frac{hc}{\lambda } - \phi - (1)

2nd Case: eV_{0} = \frac{hc}{2\lambda } - \phi - (2) \times 3

\Rightarrow 3eV_{0} = \frac{3hc}{2\lambda } - 3\phi - (3)

From equation (1) and (3)

\frac{3hc}{2\lambda } - 3\phi = \frac{hc}{\lambda } - \phi

or  2\phi = \frac{hc}{2\lambda }. 

or \phi = \frac{hc}{4\lambda }

if threshold wavelength is \lambda _{0} then 

\frac{hc}{4\lambda } 

or \lambda _{0} = 4\lambda


Option 1)

4 \lambda

Option 2)

\frac{\lambda}{4}

Option 3)

\frac{\lambda}{6}

Option 4)

6 \lambda

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