Photoelectrons are emitted when photons of energy 4.2 eV are incident on a photosensitive metallic sphere of radius 10 cm and work function 2.4 eV. The number of photoelectrons emitted before the emission is stopped is [(1)/(4πε₀) = 9 × 10⁹. SI unit; e = 1.6 × 10⁻¹⁹ C] (a) 1.25 × 10⁶ (b) 1.25 × 10² (c) 1.25 × 10⁸ (d) 1.25 × 10⁴

Answer: (c). Emission stops when the sphere potential equals the stopping potential: V = 4.2 - 2.4 = 1.8 V. V = kQ/r ⇒ Q = (1.8 × 0.1)/(9 × 10⁹) = 2 × 10⁻¹¹ C n = Q/e = 2 × 10⁻¹¹1.6 × 10⁻¹⁹ = 1.25 × 10⁸ So the answer is (c).

Photoelectrons are emitted when photons of energy 4.2 eV are incident… | MHT CET 2021 (20 Sep, Shift 2)

Q115MHT CET 2021 · 20 SEP · SHIFT 2Difficult

Photoelectric Effect: Einstein's Equation

Photoelectrons are emitted when photons of energy $4.2\text{ eV}$ are incident on a photosensitive metallic sphere of radius $10\text{ cm}$ and work function $2.4\text{ eV}$ . The number of photoelectrons emitted before the emission is stopped is

$\left[\frac{1}{4\pi\epsilon_0} = 9 \times 10^{9}\right.$ SI unit; $e = 1.6 \times 10^{-19}\text{ C}]$

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Answer: (c)

Emission stops when the sphere potential equals the stopping potential: $V = 4.2 - 2.4 = 1.8$ V.
$V = \frac{kQ}{r} \Rightarrow Q = \frac{1.8 \times 0.1}{9 \times 10^9} = 2 \times 10^{-11}$ C
$n = \frac{Q}{e} = \frac{2 \times 10^{-11}}{1.6 \times 10^{-19}} = 1.25 \times 10^8$
So the answer is (c).

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