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Dual Nature Of Radiation And Matter

Question

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When the light of frequency 2v₀ (where v₀ is threshold frequency), is incident on a metal plate, the maximum velocity of electrons emitted is v₁. When the frequency of the incident radiation is increased to 5v₀, the maximum velocity of electrons emitted from the same plate is v₂. The ratio of v₁ to v₂ is

1:2

1:4

2:1

4:1

Solution

A.

1:2

Using Einstein's photoelectric equation,

E =W₀ + k_max

When light of frequency, 2v₀ is incident on a metal plate,

$h (2 v_{o}) = h v_{o} + \frac{1}{2} m v_{1}^{2} h v_{0} = \frac{1}{2} m v_{1}^{2} . . . . . (i)$

When light of frequency, 5v₀ is incident on a metal plate

h(5v₀) = hv₀ + $\frac{1}{2} m v_{2}^{2}$

$h v_{0} = \frac{1}{2} m v_{2}^{2} . . . . (i i)$

Dividing equ (i) and (ii)

$\frac{1}{4} = \frac{v_{1}^{2}}{v_{2}^{2}} ∴ \frac{v_{1}}{v_{2}} = \frac{1}{2}$

Some More Questions From Dual Nature of Radiation and Matter Chapter

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