Photon Momentum
A beam of X-ray photons each of wavelength 0.2 nm travels toward a target, and a researcher wants the momentum carried by a single such photon.
Select the correct option:
Solution
Approximately3.3×10−24kg⋅m/s
Although a photon has no rest mass, NCERT shows that it carries momentum given by p=λh, a relation that follows from combining E=hν with the relativistic result E=pc for a massless particle. Substituting h=6.63×10−34 J·s and λ=0.2×10−9=2×10−10 m gives p=2×10−106.63×10−34=3.3×10−24 kg·m/s. This momentum, though tiny, is what allows radiation to exert pressure on surfaces. The value 3.3×10−27 kg·m/s is wrong because it mishandles the nanometre-to-metre conversion by three orders of magnitude. The value 1.3×10−24 kg·m/s is wrong because it uses an incorrect wavelength of about 0.5 nm rather than 0.2 nm. The value 6.6×10−34 kg·m/s is wrong because it merely restates Planck's constant without dividing by the wavelength. As stated in NCERT Class 12, Chapter 11, photon momentum is inversely proportional to wavelength, so short-wavelength X-rays carry substantial momentum per photon. This momentum relation also explains radiation pressure: when photons strike and are absorbed or reflected by a surface, they transfer this momentum, exerting a measurable force per unit area. Because short-wavelength X-ray photons carry far more momentum than visible photons, they interact strongly with matter and are used in techniques such as Compton scattering. A magnitude check confirms that a 0.2 nm X-ray photon should carry appreciably more momentum than a visible photon, consistent with the small wavelength.
🔒 Solution Hidden from View
Submit your answer to unlock the detailed step-by-step solution.
More photon momentum Practice Questions
About This Question
- Subject
- physics
- Chapter
- dual nature of matter and radiation
- Topic
- photon momentum
- Difficulty
- Medium
- Year
- 2025
Solution
Correct Answer:
Approximately3.3×10−24kg⋅m/s
Although a photon has no rest mass, NCERT shows that it carries momentum given by p=λh, a relation that follows from combining E=hν with the relativistic result E=pc for a massless particle. Substituting h=6.63×10−34 J·s and λ=0.2×10−9=2×10−10 m gives p=2×10−106.63×10−34=3.3×10−24 kg·m/s. This momentum, though tiny, is what allows radiation to exert pressure on surfaces. The value 3.3×10−27 kg·m/s is wrong because it mishandles the nanometre-to-metre conversion by three orders of magnitude. The value 1.3×10−24 kg·m/s is wrong because it uses an incorrect wavelength of about 0.5 nm rather than 0.2 nm. The value 6.6×10−34 kg·m/s is wrong because it merely restates Planck's constant without dividing by the wavelength. As stated in NCERT Class 12, Chapter 11, photon momentum is inversely proportional to wavelength, so short-wavelength X-rays carry substantial momentum per photon. This momentum relation also explains radiation pressure: when photons strike and are absorbed or reflected by a surface, they transfer this momentum, exerting a measurable force per unit area. Because short-wavelength X-ray photons carry far more momentum than visible photons, they interact strongly with matter and are used in techniques such as Compton scattering. A magnitude check confirms that a 0.2 nm X-ray photon should carry appreciably more momentum than a visible photon, consistent with the small wavelength.
This medium difficulty physics question is from the chapter dual nature of matter and radiation, covering the topic of photon momentum. It appeared in the 2025 exam.
Looking for more practice? Explore all physics questions or browse dual nature of matter and radiation questions on RankGuru.