Question:
A copper ball of radius 1 cm and work function 4.47 eV is irradiated with ultraviolet radiation of wavelength 2500 \(\mathrm{\AA}\). The effect of irradiation results in the emission of electrons from the ball. Further the ball will acquire charge and due to this there will be a finite value of the potential on the ball. The charge acquired by the ball is :
A copper ball of radius 1 cm and work function 4.47 eV is irradiated with ultraviolet radiation of wavelength 2500 \(\mathrm{\AA}\). The effect of irradiation results in the emission of electrons from the ball. Further the ball will acquire charge and due to this there will be a finite value of the potential on the ball. The charge acquired by the ball is :
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Emission stops when the ball's potential equals the stopping potential \(V_0 = (E_{photon}-\phi)/e\); then \(Q = 4\pi\epsilon_0 R V_0\).
Updated On: Nov 4, 2026
- \(5.5\times10^{-13}\) C
- \(7.5\times10^{-13}\) C
- \(4.5\times10^{-12}\) C
- \(2.5\times10^{-11}\) C
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The Correct Option is A
Solution and Explanation
Photon energy \(E = \dfrac{12400\ \mathrm{eV\,\AA}}{2500\ \mathrm{\AA}} = 4.96\) eV.
Maximum kinetic energy \(K = 4.96 - 4.47 = 0.49\) eV.
Electrons leave until the ball's potential rises to the stopping potential, \(V = 0.49\) V.
Potential of a charged sphere: \(V = \dfrac{Q}{4\pi\epsilon_0 R}\), so \(Q = 4\pi\epsilon_0 R V = \dfrac{0.01\times0.49}{9\times10^{9}}\).
\(Q \approx 5.4\times10^{-13}\) C \(\approx 5.5\times10^{-13}\) C.
Answer: (1) \(5.5\times10^{-13}\) C
Maximum kinetic energy \(K = 4.96 - 4.47 = 0.49\) eV.
Electrons leave until the ball's potential rises to the stopping potential, \(V = 0.49\) V.
Potential of a charged sphere: \(V = \dfrac{Q}{4\pi\epsilon_0 R}\), so \(Q = 4\pi\epsilon_0 R V = \dfrac{0.01\times0.49}{9\times10^{9}}\).
\(Q \approx 5.4\times10^{-13}\) C \(\approx 5.5\times10^{-13}\) C.
Answer: (1) \(5.5\times10^{-13}\) C
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