State Einstein's photoelectric equation. Explain any two characteristics of photoelectric effect on the basis of this equation.
(July 2018)
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Einstein’s photoelectric equation:$K.E._{max} = (hν – φ_0)$
Two characteristics of the photoelectric effect:
1. The photoelectric work function $φ_0$ is constant for a given emitter. Hence if the frequency ‘ν’ of the incident radiation is decreased, the maximum kinetic energy of the emitted photoelectrons decreases, till it becomes zero for a certain frequency $ν_0$. Therefore, from Einstein’s equation,
\(0= hv _0-\phi_0\)
\(\therefore \phi_0= hv _0\).....….(1)
This shows that the threshold frequency is related to the work function of the metal and hence it has different values for different metals.
2. The photoelectric equation is,
\(\frac{1}{2} m v_{\max }^2=h v-\phi_0\)....….(2)
where, hν = energy of the photon of incident radiation.
\(\phi_0=h v_0=\)photoelectric work function of the metal.
Thus, both the terms on the R.H.S of equation (2) depends on the frequency and not on the intensity of radiation. Hence, the maximum kinetic energy with which photoelectrons are emitted is independent of the intensity of radiation. However, since φ0 and h are constants, the maximum kinetic energy of the photoelectrons is directly proportional to the frequency.
Two characteristics of the photoelectric effect:
1. The photoelectric work function $φ_0$ is constant for a given emitter. Hence if the frequency ‘ν’ of the incident radiation is decreased, the maximum kinetic energy of the emitted photoelectrons decreases, till it becomes zero for a certain frequency $ν_0$. Therefore, from Einstein’s equation,
\(0= hv _0-\phi_0\)
\(\therefore \phi_0= hv _0\).....….(1)
This shows that the threshold frequency is related to the work function of the metal and hence it has different values for different metals.
2. The photoelectric equation is,
\(\frac{1}{2} m v_{\max }^2=h v-\phi_0\)....….(2)
where, hν = energy of the photon of incident radiation.
\(\phi_0=h v_0=\)photoelectric work function of the metal.
Thus, both the terms on the R.H.S of equation (2) depends on the frequency and not on the intensity of radiation. Hence, the maximum kinetic energy with which photoelectrons are emitted is independent of the intensity of radiation. However, since φ0 and h are constants, the maximum kinetic energy of the photoelectrons is directly proportional to the frequency.
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