Photon — Energy, momentum
Dual Nature of Matter
10
JEE Qs
8%
Hard
45
min
Master the interconversion between energy, momentum, frequency, and wavelength of a photon using the fundamental constants h and c, and always pay close attention to unit conversions.
🧮 Key Formulas
✅ Key Points for JEE
- 1Photons are elementary particles of light, carrying a discrete amount of energy (quanta) and momentum.
- 2They have zero rest mass but possess both energy and momentum, traveling at the speed of light 'c' in a vacuum.
- 3The energy and momentum of a photon are directly proportional to its frequency and inversely proportional to its wavelength.
- 4The number of photons in a given interaction (e.g., absorption, emission) is generally not conserved, unlike conserved quantities like total energy and momentum.
- 5The relativistic energy-momentum relation E = pc applies to massless particles like photons.
⚠️ Common Mistakes
- ✕Forgetting to convert units (e.g., eV to J, nm to m) before calculations, leading to incorrect numerical answers.
- ✕Confusing the intensity of light (power per unit area) with the energy of a single photon; intensity depends on the number of photons, not just individual photon energy.
- ✕Neglecting the momentum of photons, especially when dealing with concepts like radiation pressure or momentum transfer during absorption/emission events.
📝 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