The work function of caesium metal is 2.14 eV. When light of frequency 6 × 1014 Hz is incident on the metal surface, photoemission of electrons occurs. What is the
(a) maximum kinetic energy of the emitted electrons
(b) Stopping potential
(c) maximum speed of the emitted photoelectrons?
Work function of caesium, $\Phi_{o}=2.14 \mathrm{eV}$
Frequency of light, $\mathrm{v}=6.0 \times 10^{14} \mathrm{~Hz}$
(a) The maximum energy (kinetic) by the photoelectric effect:
$\mathrm{K}=\mathrm{hv}-\Phi_{o}$
h = Planck’s constant = 6.626 x 10-34 Js
Therefore,
$K=\frac{6.626 \times 10^{-34} \times 6 \times 10^{14}}{1.6 \times 10^{-19}}-2.14$
$=2.485-2.140=0.345 \mathrm{eV}$
Hence, 0.345 eV is the maximum kinetic energy of the emitted electrons.
(b) For stopping potential Vo, we can write the equation for kinetic energy as:
K = eVo
Therefore, $\mathrm{V}_{0}=\frac{K}{e}$
$=\frac{0.345 \times 1.6 \times 10^{-19}}{1.6 \times 10^{-19}}$
= 0.345 V
Hence, 0.345 V is the stopping potential of the material.
(c) Maximum speed of photoelectrons emitted = ν
Following is the kinetic energy relation:
$\mathrm{K}=\frac{1}{2} m v^{2}$
Where,
m = mass of electron = 9.1 x 10-31 Kg
$v^{2}=\frac{2 K}{m}$
$=\frac{2 \times 0.345 \times 1.6 \times 10^{-19}}{9.1 \times 10^{-31}}$
=0.1104 x 1012
Therefore, ν = 3.323 x 105 m/s = 332.3 km/s
Hence, 332.3 km/s is the maximum speed of the emitted photoelectrons.
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- JEE Main
- Exam Pattern
- Previous Year Papers
- PYQ Chapterwise
- Physics
- Kinematics 1D
- Kinemetics 2D
- Friction
- Work, Power, Energy
- Centre of Mass and Collision
- Rotational Dynamics
- Gravitation
- Calorimetry
- Elasticity
- Thermal Expansion
- Heat Transfer
- Kinetic Theory of Gases
- Thermodynamics
- Simple Harmonic Motion
- Wave on String
- Sound waves
- Fluid Mechanics
- Electrostatics
- Current Electricity
- Capacitor
- Magnetism and Matter
- Electromagnetic Induction
- Atomic Structure
- Dual Nature of Matter
- Nuclear Physics
- Radioactivity
- Semiconductors
- Communication System
- Error in Measurement & instruments
- Alternating Current
- Electromagnetic Waves
- Wave Optics
- X-Rays
- All Subjects
- Physics
- Motion in a Plane
- Law of Motion
- Work, Energy and Power
- Systems of Particles and Rotational Motion
- Gravitation
- Mechanical Properties of Solids
- Mechanical Properties of Fluids
- Thermal Properties of matter
- Thermodynamics
- Kinetic Theory
- Oscillations
- Waves
- Electric Charge and Fields
- Electrostatic Potential and Capacitance
- Current Electricity
- Thermoelectric Effects of Electric Current
- Heating Effects of Electric Current
- Moving Charges and Magnetism
- Magnetism and Matter
- Electromagnetic Induction
- Alternating Current
- Electromagnetic Wave
- Ray Optics and Optical Instruments
- Wave Optics
- Dual Nature of Radiation and Matter
- Atoms
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- Chemical Effects of Electric Current,