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Chapter 17: Problem 2385

In photo electric effect, if threshold wave length of a metal is \(5000 \AA\) work function of this metal is ..........V. $\left(\mathrm{h}=6.62 \times 10^{-34} \mathrm{~J} . \mathrm{s}, \mathrm{c}=3 \times 10^{8} \mathrm{~m} / \mathrm{s}, 1 \mathrm{eV}=1.6 \times 10^{-19} \mathrm{~J}\right)$ (A) \(1.24\) (B) \(2.48\) (C) \(4.96\) (D) \(3.72\)

Short Answer

Expert verified
The work function of the metal is approximately \(2.49 \, eV\), which corresponds to option (B) \(2.48 \, eV\).

Step by step solution

01

Write down the threshold wavelength and the given constants

We are given the threshold wavelength λ, Planck's constant h, the speed of light c, and the conversion factor between electron volts and joules (1 eV = 1.6 x 10^-19 J). Let's note them. Threshold wavelength, λ = 5000 Ǻ Planck's constant, h = 6.62 x 10^-34 Js Speed of light, c = 3 x 10^8 m/s
02

Convert the threshold wavelength to meters

The threshold wavelength λ is given in angstroms (Ǻ). We need to convert it to meters (m) to match the SI units. 1 Ǻ = 10^-10 m So, λ = 5000 Ǻ x 10^-10 m/Ǻ = 5 x 10^-7 m
03

Use the photoelectric effect equation to find the energy of the photons

According to the photoelectric effect, the energy E of the photons in terms of the wavelength λ can be calculated by the following equation: E = h * (c / λ) Substitute the given values into the equation: E = (6.62 x 10^-34 Js) * (3 x 10^8 m/s) / (5 x 10^-7 m) E = 3.98 x 10^-19 J
04

Convert the energy to eV (electron volts)

Finally, we need to convert the energy from Joules (J) to electron volts (eV). Remember, 1eV = 1.6 x 10^-19 J. So, E (eV) = E (J) / (1.6 x 10^-19 J/eV) E (eV) = (3.98 x 10^-19 J) / (1.6 x 10^-19 J/eV) E (eV) ≈ 2.49 eV It is clear that the work function of this metal is approximately 2.49 eV, which corresponds to option (B) 2.48 eV.

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Most popular questions from this chapter

Power produced by a star is \(4 \times 10^{28} \mathrm{~W}\). If the average wavelength of the emitted radiations is considered to be \(4500 \AA\) the number of photons emitted in \(1 \mathrm{~s}\) is \(\ldots \ldots\) (A) \(1 \times 10^{45}\) (B) \(9 \times 10^{46}\) (C) \(8 \times 10^{45}\) (D) \(12 \times 10^{46}\)

\(2 \mathrm{nW}\) light of wave length \(4400 \AA\) is incident on photo sensitive surface of \(\mathrm{Cs}\). If quantum efficiency is \(0.5 \%\), what will be the value of photoelectric current? (A) \(1.56 \times 10^{-6} \mu \mathrm{A}\) (B) \(2.56 \times 10^{-6} \mu \mathrm{A}\) (C) \(4.56 \times 10^{-6} \mu \mathrm{A}\) (D) \(3.56 \times 10^{-6} \mu \mathrm{A}\)

Calculate the energy of a photon of radian wavelength \(6000 \AA\) in \(\mathrm{eV}\) (A) \(20.6 \mathrm{eV}\) (B) \(2.06 \mathrm{eV}\) (C) \(1.03 \mathrm{eV}\) (D) \(4.12 \mathrm{eV}\)

Matching type questions: (Match, Column-I and Column-II property) Column-I Column-II (I) Energy of photon of wavelength \(\lambda\) is (P) \((\mathrm{E} / \mathrm{p})\) (II) The de Broglie wavelength associated (Q) \(\left(\mathrm{hf} / \mathrm{c}^{2}\right)\) with particle of momentum \(\mathrm{P}\) is (II) Mass of photon in motion is (R) (hc \(/ \lambda\) ) (IV) The velocity of photon of energy (S) \((\mathrm{h} / \mathrm{p})\) \(\mathrm{E}\) and momentum \(\mathrm{P}\) is (A) I - P, II - Q. III - R, IV - S (B) $\mathrm{I}-\mathrm{R}, \mathrm{II}-\mathrm{S}, \mathrm{III}-\mathrm{Q}, \mathrm{IV}-\mathrm{P}$ (C) $\mathrm{I}-\mathrm{R}, \mathrm{II}-\mathrm{S}, \mathrm{III}-\mathrm{P}_{3} \mathrm{IV}-\mathrm{Q}$ (D) $\mathrm{I}-\mathrm{S}, \mathrm{II}-\mathrm{R}, \mathrm{III}-\mathrm{Q}, \mathrm{IV}-\mathrm{P}$

A proton, a deuteron and an \(\propto\) -particle having the same momentum, enters a region of uniform electric field between the parallel plates of a capacitor. The electric field is perpendicular to the initial path of the particles. Then the ratio of deflections suffered by them is (A) \(1: 2: 8\) (B) \(1: 2: 4\) (C) \(1: 1: 2\) (D) None of these
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