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Dual Nature of Radiation question

2013 · Shift 0 · Q50
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Dual Nature of Radiation question

2013 · Shift 0 · Q50

JEE MainPhysicsDual Nature of RadiationMCQ+4 / −1
The anode voltage of a photocell is kept fixed. The wavelength λ\lambdaλ of the light falling on the cathode is gradually changed. The plate current III of the photocell varies as follows :
  1. A
    JEE Main 2013 (Offline) Physics - Dual Nature of Radiation Question 174 English Option 1
  2. B
    JEE Main 2013 (Offline) Physics - Dual Nature of Radiation Question 174 English Option 2
  3. C
    JEE Main 2013 (Offline) Physics - Dual Nature of Radiation Question 174 English Option 3
  4. D
    JEE Main 2013 (Offline) Physics - Dual Nature of Radiation Question 174 English Option 4
View written solutionFree

Correct answer: D

  1. In a photocell, when the anode voltage is kept fixed, the plate current depends mainly on the number of photoelectrons emitted per second that are collected by the anode.

  2. As the wavelength λ\lambdaλ of incident light is changed:

    • For λ>λ0\lambda > \lambda_0λ>λ0​ (where λ0\lambda_0λ0​ is the threshold wavelength), the photon energy is E=hcλ<ϕE = \frac{hc}{\lambda} < \phiE=λhc​<ϕ so no photoelectric emission takes place. Hence, I=0I = 0I=0
  3. For λ<λ0\lambda < \lambda_0λ<λ0​, photoemission occurs. If the intensity of light is taken as fixed, then as wavelength decreases, energy per photon increases: E=hcλE = \frac{hc}{\lambda}E=λhc​ so the number of incident photons per second decreases. Since photocurrent is proportional to the number of emitted electrons per second, the photocurrent decreases as λ\lambdaλ decreases.

  4. Therefore, the graph of plate current III versus wavelength λ\lambdaλ should be:

    • zero for λ>λ0\lambda > \lambda_0λ>λ0​,
    • nonzero for λ<λ0\lambda < \lambda_0λ<λ0​,
    • increasing with increasing λ\lambdaλ up to the threshold,
    • and then suddenly dropping to zero at λ=λ0\lambda = \lambda_0λ=λ0​.
  5. Among the given options, this corresponds to Option D.

Thus, the correct choice is: D\boxed{D}D​

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