JEE Main · Physics ↓ Falling

Dual Nature of Radiation and Matter appeared 31 times across 3 years — 3.6% of Physics. This question is from Photoelectric Effect and Threshold Frequency.

Year 2026 2025 2024 Total
Questions 7 16 8 31
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Light is incident on a metallic plate having work function 110 × 10⁻²⁰ J. If the produced photoelectrons have zero kinetic energy then the angular frequency of the incident light is ____ rad/s. (h = 6.63 × 10⁻³⁴ J.s)

Solution & Explanation

Related Formula

φ = h v

ω = 2π v = (2π φ)/(h)
Core Logic

Since kinetic energy of photoelectrons is zero (Kmax = 0), incident photon energy equals work function φ:

h v = φ v = (φ)/(h)

Calculating angular frequency ω:

ω = 2π v = (2π φ)/(h) = 2 × 3.14 × 110 × 10⁻²⁰6.63 × 10⁻³⁴ ω = 690.8 × 10⁻²⁰6.63 × 10⁻³⁴ ≈ 1.04 × 10¹⁶ ~rad/s
Step 1: Final Conclusion

The angular frequency of incident light is 1.04 × 10¹⁶ ~rad/s.

Pattern Recognition

Zero kinetic energy hν = φ. Convert linear frequency ν to angular frequency ω = 2π φ / h.

Chapter Mix

Class 12 Physics: Dual Nature of Radiation and Matter

Reference Study Guides

Dual Nature Of Radiation And Matter

More Dual Nature of Radiation and Matter Previous-Year Questions — Page 7

Q50 jee_main_2024_31_jan_morning Photoelectric Effect
When a metal surface is illuminated by light of wavelength λ, the stopping potential is 8 V. When the same surface is illuminated by light of wavelength 3λ, stopping potential is 2 V. The threshold wavelength for this surface is:
  • A. 5λ
  • B. 3λ
  • C. 9λ
  • D. 4.5λ

Solution

Related Formula
(hc)/(λ) = φ + Kmax Kmax = eV₀ φ = (hc)/(λ₀)
Core Logic

Using Einstein's Photoelectric equation for the two cases:

Case 1 (Wavelength λ, Stopping Potential 8 V):

(hc)/(λ) = (hc)/(λ₀) + 8e (i)

Case 2 (Wavelength 3λ, Stopping Potential 2 V):

(hc)/(3λ) = (hc)/(λ₀) + 2e (ii)
Step 2: Solving the Equations

Multiply equation (ii) by 4 to eliminate e:

(4hc)/(3λ) = (4hc)/(λ₀) + 8e

Equating this to equation (i):

(hc)/(λ) - (hc)/(λ₀) = (4hc)/(3λ) - (4hc)/(λ₀)

Divide entirely by hc:

(1)/(λ) - (1)/(λ₀) = (4)/(3λ) - (4)/(λ₀) (4)/(λ₀) - (1)/(λ₀) = (4)/(3λ) - (1)/(λ) (3)/(λ₀) = (4 - 3)/(3λ) (3)/(λ₀) = (1)/(3λ) λ₀ = 9λ
Chapter Mix

Class 12 Physics: Dual Nature Of Radiation And Matter

More Dual Nature of Radiation and Matter Questions — jee_main_2026_22_january_evening

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Rankbit System
JEE Physics: Waves (+15.5%) | Electrostatics: Concentric Shells (-29.7%) | Modern Physics: Photoelectric Clones (+34.2%) | Mathematics: Definite Integrals (+18.1%) | Chemistry: Coordination Splitting (-11.4%) | JEE Physics: Waves (+15.5%) | Electrostatics: Concentric Shells (-29.7%) | Modern Physics: Photoelectric Clones (+34.2%) | Mathematics: Definite Integrals (+18.1%) | Chemistry: Coordination Splitting (-11.4%)