Ultraviolet light of wavelength 2271 Å from a 100 W mercury source irradiates a photo-cell made of molybdenum metal.
Ultraviolet light of wavelength 2271 Å from a 100 W mercury source irradiates a photo-cell made of molybdenum metal. If the stopping potential is −1.3 V, estimate the work function of the metal. How would the photo-cell respond to a high intensity (∼105 W m−2) red light of wavelength 6328 Å produced by a He-Ne laser?
Wavelength of ultraviolet light, λ = 2271 Å = 2271 × 10−10 m
Stopping potential of the metal, V0 = 1.3 V
Planck’s constant, h = 6.6 × 10−34 J
Charge on an electron, e = 1.6 × 10−19 C
Work function of the metal $=\phi_{0}$
Frequency of light = ν
We have the photo-energy relation from the photoelectric effect as
$\phi_{0}=h v-e V_{0}$
$=\frac{h c}{\lambda}-e V_{0}$
$=\frac{6.6 \times 10^{-34} \times 3 \times 10^{8}}{2271 \times 10^{-10}}-1.6 \times 10^{-19} \times 1.3$
$=8.72 \times 10^{-19}-2.08 \times 10^{-19}$'
$=6.64 \times 10^{-19} \mathrm{~J}$
$=\frac{6.64 \times 10^{-19}}{1.6 \times 10^{-19}}=4.15 \mathrm{eV}$
Let ν0 be the threshold frequency of the metal.
$\therefore \phi_{0}=h v_{0}$
$v_{0}=\frac{\phi_{0}}{h}$
$=\frac{6.64 \times 10^{-19}}{6.6 \times 10^{-34}}=1.006 \times 10^{15} \mathrm{~Hz}$
Wavelength of red light, = 6328 × 10−10 m
$\therefore$ Frequency of red light, $v_{r}=\frac{c}{\lambda_{r}}$
$=\frac{3 \times 10^{8}}{6328 \times 10^{-10}}=4.74 \times 10^{14} \mathrm{~Hz}$
Since ν0> νr, the photocell will not respond to the red light produced by the laser.
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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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- Semiconductor Electronics: Materials, Devices and Simple Circuits.
- Chemical Effects of Electric Current,