CBSE Class 12 · 2015 · Delhi · Modern PhysicsShort Answer

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Write Einstein's photoelectric equation and mention which important features in the photoelectric effect can be explained with the help of this equation. The maximum kinetic energy of the photoelectrons gets doubled when the wavelength of light incident on the surface changes from

λ_{1}

λ_{2}

. Derive the expressions for the threshold wavelength

λ_{0}

and work function for the metal surface.

Answer: $ϕ_{0} = h c (2/ λ_{1} - 1/ λ_{2})$ ; $λ_{0} = λ_{1} λ_{2} / (2 λ_{2} - λ_{1})$ .

Solution

Einstein's equation:

K_{ma x} = \frac{h c}{λ} - ϕ_{0}

; it explains the threshold frequency, the linear dependence of

K_{ma x}

on frequency and the instantaneous emission.
For the two wavelengths, with

K_{2} = 2 K_{1}

K_{1} = \frac{h c}{λ _{1}} - ϕ_{0}, K_{2} = \frac{h c}{λ _{2}} - ϕ_{0} = 2 (\frac{h c}{λ _{1}} - ϕ_{0}) .

Solving for the work function:

ϕ_{0} = h c (\frac{2}{λ _{1}} - \frac{1}{λ _{2}}) .

Threshold wavelength

λ_{0} = \frac{h c}{ϕ _{0}}

λ_{0} = \frac{λ _{1} λ _{2}}{2 λ _{2} - λ _{1}}, ϕ_{0} = h c (\frac{2}{λ _{1}} - \frac{1}{λ _{2}})

CBSE Class 12 Board · 2015 · Delhi · Subjective

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CBSE Class 12 · 2015 · Delhi · Modern PhysicsShort Answer

Solution

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