The photoelectric current will flow only if:

  1. The wavelength of incident radiation is above the threshold value
  2. The wavelength of incident radiation is below the threshold value
  3. The intensity of incident radiation is above the threshold value
  4. The intensity of incident radiation is below the threshold value

Answer (Detailed Solution Below)

Option 2 : The wavelength of incident radiation is below the threshold value
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CONCEPT:

F1 J.K 3.8.20 Pallavi D6

Photoelectric Effect:

  • When the light of a sufficiently small wavelength is incident on the metal surface, electrons are ejected from the metal instantly. This phenomenon is called the photoelectric effect.​
  • Einstein’s photoelectric equation:

⇒ KEmax = E - ϕo

\(⇒ KE_{max}=\frac{hc}{λ}-\frac{hc}{λ_o}\)

Where h = Planck's constant = 6.6 × 10-34 J-sec, λ = wavelength of photon, λo = threshold wavelength, and KE = maximum kinetic energy of electrons.

Laws of Photoelectric Effect:

  1. For a light of any given frequency; (f > fTh) photoelectric current is directly proportional to the intensity of light
  2. For any given material, there is a certain minimum frequency, called threshold frequencybelow which the emission of photoelectrons stops completely, no matter how high is the intensity of incident light.
  3. The maximum kinetic energy of the photoelectrons is found to increase with the increase in the frequency of incident light, provided the frequency (f > fTh) exceeds the threshold limit. The maximum kinetic energy is independent of the intensity of light.
  4. The photoelectric emission is an instantaneous process without any apparent time lag (10-9 sec or less), even when the intensity of the incident radiation is made extremely low.​​

EXPLANATION:

  • Einstein’s photoelectric equation is given as,

\(⇒ KE_{max}=\frac{hc}{λ}-\frac{hc}{λ_o}\)     -----(1)

Where λ = wavelength of the photon, and λo = threshold wavelength

By equation 1, for the photoelectric effect,

⇒ KEmax > 0

\(⇒ \frac{hc}{λ}>\frac{hc}{λ_o}\)

⇒ λ < λo     -----(2)

  • ​So by equation 2, we can say that ​the photoelectric current will flow only if the wavelength of incident radiation is below the threshold value. Hence, option 2 is correct.
 
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