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Question

The graph between 1/λ and stopping potential (V) of three metals having work functions ϕ1, ϕ2 and ϕ3 in an experiment of photo-electric effect is plotted as shown in the figure. 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
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B
Ratio of work functions ϕ1 : ϕ2 : ϕ3=4 : 2 : 1
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C
tanΘ is directly proportional to hc/e, where h is Planck's constant and c is the speed of light.
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D
The violet colour light can eject photoelectrons from metals 2 and 3.
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Solution

The correct options are
A Ratio of work functions ϕ1 : ϕ2 : ϕ3=1 : 2 : 4
C tanΘ is directly proportional to hc/e, where h is Planck's constant and c is the speed of light.
From photo electric effect, eV=hcλϕ where V= stopping potential and ϕ= work function.
Slope , m=tanθ=hc/e (compare above equation with y=mxc)

If V=0ϕhc=1λ

Now from given graph,

for metal 1 : ϕ1hc=0.001

for metal 2: ϕ2hc=0.002

for metal 3: ϕ3hc=0.004

Thus, ϕ1:ϕ2:ϕ3=1:2:4

Also, ϕ=hcλ0 where λ0 be the threshold wavelength.

For metal 2 : λ02=1/0.002=500nm
For metal 3 : λ02=1/0.004=250nm
As the wavelength of violet colour is around 400 nm so only metal 2 can eject violet colour light but not metal 3.
Thus, options A and C is right.

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