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Question:

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?

1:4

2:1

4:1

1:2

Solution:

We know that, K.E. = hν - φ₀ where φ₀ can be written as hv₀
When ν = 2v₀
K.E.₁ = mv₁²/2 = 2hv₀ - hv₀
v₁ = √(2hv₀/m)
Similarly we can find that
v₂ = √(4hv₀/m)
Hence, v₁/v₂ = 1/2