de Broglie wavelength of accelerated particles
Dual Nature of Matter
10
JEE Qs
8%
Hard
60
min
Master the derivation of de Broglie wavelength for an accelerated charged particle from fundamental principles and be precise with unit conversions for accurate results.
🧮 Key Formulas
✅ Key Points for JEE
- 1The de Broglie wavelength (λ) is inversely proportional to the momentum (p) of the particle (λ ∝ 1/p).
- 2For charged particles accelerated from rest through a potential difference V, their kinetic energy K = qV. Substitute this into the de Broglie wavelength formula.
- 3The de Broglie wavelength is significant for microscopic particles like electrons, protons, and alpha particles, but negligible for macroscopic objects due to their large momentum.
- 4Be careful with units: use SI units (Joules for energy, Coulombs for charge, meters for wavelength, kg for mass) unless a specific formula (like for electron) uses different units and provides a direct conversion.
⚠️ Common Mistakes
- ✕Confusing potential difference (V) with velocity (v) in formulas and calculations.
- ✕Incorrectly using mass 'm' for different particles (electron, proton, alpha particle) or using electron rest mass when relativistic effects might be relevant (though usually ignored in basic JEE problems).
- ✕Errors in unit conversion, especially between electron volts (eV) and Joules (J), or angstroms (Å) and meters (m).
📝 Practice Questions
See allQ42.A light source of wavelength λ illuminates a metal surface and electrons are ejected with maximum kinetic energy of 2 eV . If the same surface is illuminated by a light source of wavelength λ , then the maximum 2 kinetic energy of ejected electrons will be (The work function of metal is 1 eV ) (1) 3 eV (2) 2 eV (3) 6 eV (4) 5 eV
Q45.In photoelectric effect an em-wave is incident on a metal surface and electrons are ejected from the surface. If the work function of the metal is 2.14 eV and stopping potential is 2 V , what is the wavelength of the em- wave ? (Given hc = 1242eVnm where h is the Planck's constant and c is the speed of light in vaccum.) 2025 (23 Jan Shift 2) JEE Main Previous Year Paper (1) 300 nm (2) 400 nm (3) 600 nm (4) 200 nm
Q30.An electron in the ground state of the hydrogen atom has the orbital radius of 5.3 × 10−11 m while that for the electron in third excited state is 8.48 × 10−10 m . The ratio of the de Broglie wavelengths of electron in the excited state to that in the ground state is (1) 3 (2) 16 (3) 9 (4) 4
Q40.The work functions of cesium (Cs) and lithium (Li) metals are 1.9 eV and 2.5 eV , respectively. If we incident a light of wavelength 550 nm on these two metal surfaces, then photo-electric effect is possible for the case of (1) Both Cs and Li (2) Neither Cs nor Li (3) Cs only (4) Li only
Q34.A sub-atomic particle of mass 10−30 kg is moving with a velocity 2.21 × 106 m/s. Under the matter wave consideration, the particle will behave closely like (h = 6.63 × 10−34 J. s) (1) Visible radiation (2) Gamma rays (3) Infra-red radiation (4) X-rays
Q32.An electron of mass ' m ' with an initial velocity →v = v0^i (v0 > 0) enters an electric field E = −Eo^k . If the initial de Broglie wavelength is λ0 , the value after time t would be (1) λ0 (2) e2E20t2 m2v2o √1+ e2E02t2m2v02 λo√1 + (3) λ0 (4) λ0 √1−e2Eo2t2m2v2o
NCERT Chapters
- Class 12 Physics Ch 11: Dual Nature of Radiation and Matter
- Class 12 Physics Ch 2: Electrostatic Potential and Capacitance