Question 230: Dual Nature of Matter and Radiation

Question

When light of frequency twice the threshold frequency is incident on the metal plate, the maximum velocity of emitted electron is v
1
. When the frequency of incident radiation is increased to five times the threshold value, the maximum velocity of emitted electron becomes v
2
. If v
2
= x v
1
, the value of x will be __________.

Accepted Answer

Let us say that work function is $$\phi$$
$$ \Rightarrow 2\phi  = \phi  + {1 \over 2}mv_1^2$$ ...... (1)
and $$5\phi  = \phi  + {1 \over 2}mv_2^2$$ ..... (2)
From (1) and (2)
$${{v_2^2} \over {v_1^2}} = {4 \over 1}$$ or $${{{v_2}} \over {{v_1}}} = 2$$

Dual Nature of Matter and Radiation

Integer / Numeric Answer Type