Dual Nature of Radiation and Matter - Result Question 46

48. When photons of energy $h v$ fall on an aluminium plate (of work function $E_0$ ), photoelectrons of maximum kinetic energy $K$ are ejected. If the frequency of the radiation is doubled, the maximum kinetic energy of the ejected photoelectrons will be

[2006]

(a) $2 K$

(b) $K$

(c) $K+h v$

(d) $K+E_0$

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Answer:

Correct Answer: 48. (c)

Solution:

  1. (c) Applying Einstein’s formula for photoelectricity

$h v=\phi+\frac{1}{2} m v^{2} ; \quad h v=\phi+K$

$\phi=h v-K$

If we use $2 v$ frequency then let the kinetic energy becomes $K^{\prime}$

So, $h .2 v=\phi+K$

$2 h v=h v-K+K^{\prime}$

$K^{\prime}=h v+K$