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Q.

The graph between 1/λ and stopping potential (𝒱) of three metals having work functions   ϕ1, ϕ2 and  ϕ3  in an experiment of photoelectric effect is plotted as shown in the figure.

Question Image  
Which of  the following statement(s)is / are correct? (Here, λ is the wavelength of the incident ray).
 

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a

Ratio of work functions  ϕ1:ϕ2:ϕ3=1:2:4

b

Ratio of work functions  ϕ1:ϕ2:ϕ3=4:2:1

c

tanθ  is directly proportional to hce,   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

From the equation of photoelectric effect.
 eV=hcλϕ  or  V=(hce)(1λ)ϕe
This is equation of straight line.
 Y=mx+c
Slope is  tanθ=hce
 ϕ1:ϕ2:ϕ3=hcλ01:λcλ02:hcλ03 =hcλ01:λcλ02:hcλ03=1:2:4 hcλ01=0.001nm1  or  λ01=10000A0 hcλ02=0.002nm1  or   λ02=5000A0 hcλ03=0.004nm1  or   λ03=2500A0
 
 
 
 
Violet colour has wavelength 4000A0  . So, violet colour can eject photoelectrons from metal-1 and metal-2
 

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