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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].
42756.jpg
  1. Ratio of work functions ϕ1 : ϕ2 : ϕ3=1 : 2 : 4
  2. Ratio of work functions ϕ1 : ϕ2 : ϕ3=4 : 2 : 1
  3. tanΘ is directly proportional to hc/e, where h is Planck's constant and c is the speed of light.
  4. The violet colour light can eject photoelectrons from metals 2 and 3.

A
tanΘ is directly proportional to hc/e, where h is Planck's constant and c is the speed of light.
B
Ratio of work functions ϕ1 : ϕ2 : ϕ3=1 : 2 : 4
C
Ratio of work functions ϕ1 : ϕ2 : ϕ3=4 : 2 : 1
D
The violet colour light can eject photoelectrons from metals 2 and 3.
Solution
Verified by Toppr

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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The graph 1λ and stopping potential (V) of three metals having work function ϕ1, ϕ2 and ϕ3 in an experiment of photoelectric effect is plotted as shown in the figure. Which one of the following statement is/are correct? [Here λ is the wavelength of the incident ray]
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(ii) Ratio of work functions ϕ1:ϕ2:ϕ3=4:2:1
(iii) tanθhce, where h= Planck's constant, c= speed of light
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