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Q.

The graph detween 1/ λ, and stopping potential (V) of three metals having work functions f1, f2 and f3 in an experiment of photo-electric effect is plotted as shown in the figure. Which of the following statement(s) is/are correct?

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a

Ratio of work functions f1:f2:f3=1:2:4

b

Ratio of work functions  f1:f2:f3=4:2:1

c

tanθ is directly proportional to hc/e, where h is Planck's constant and c is the speed of light

d

The violet colour light can eject photoelectrons from metals 2 and 3.

answer is A, C.

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Detailed Solution

According to Einstein’s photoelectric equation

hcλo=eVwhereo=workfunction

Vand(1λ) relation represents a straight line

Slope of line=hceortanθ=hce

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At V0=0, λ=λ0,ϕ=hcλ

ϕ1:ϕ2:ϕ3=hcλ01:hcλ02:hcλ03=0.001:0.002:0.004=1:2:4

1λ01=0.001nm-1λ01=10-6m

1λ02=0.002nm-1λ02=0.5×10-6m

1λ03=0.004nm-1λ03=0.25×10-6m

Now λviolet=0.4x10-6m

For ejection of photoelectrons,

λviolet<λ0

So, violet colour can eject photoelectrons from metals 1, 2 but not from metal 3

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