When radiation of wavelength $\lambda$ is incident on a metallic surface, the stopping potential of ejected photoelectrons is $4.8 \mathrm{~V}$. If the same surface is illuminated by radiation of double the previous wavelength, then the stopping potential becomes $1.6 \mathrm{~V}$. The threshold wavelength of the metal is :
$2 \lambda$
$4 \lambda$
$8 \lambda$
$6 \lambda$
Correct Option: , 2
$\mathrm{V}_{\mathrm{S}}=\mathrm{h} v-\phi$
$4.8=\frac{\mathrm{hc}}{\lambda}-\phi$..(1)
$1.6=\frac{\mathrm{hc}}{2 \lambda}-\phi$..(2)
Using above equation (i) - (ii)
$3.2=\frac{\mathrm{hc}}{\lambda}-\frac{\mathrm{hc}}{2 \lambda}$
$3.2=\frac{\mathrm{hc}}{2 \lambda}$..(3)
$\left[\lambda=\frac{\mathrm{hc}}{6.4}\right]$
Put in equation (ii)
$\phi=1.6$
$\frac{\mathrm{hc}}{\lambda_{\mathrm{th}}}=1.6$
$\lambda_{\text {th }}=\frac{\text { hc }}{1.6}$
$=\left(\frac{\mathrm{hc}}{6.4}\right) \times 4=4 \lambda$
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All Study Material
- 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
- Nuclei
- Semiconductor Electronics: Materials, Devices and Simple Circuits.
- Chemical Effects of Electric Current,