Photon Energy
A green laser pointer used in a classroom emits light of wavelength 500 nm, and a student wants the energy carried by each individual photon in the beam.
Select the correct option:
Solution
Approximately 3.98 × 10⁻¹⁹ J
Each photon carries energy given in NCERT by E=λhc, where h=6.63×10−34 J·s is Planck's constant, c=3×108 m/s is the speed of light, and λ is the wavelength. Substituting λ=500×10−9 m gives E=500×10−9(6.63×10−34)(3×108)=5×10−71.989×10−25=3.98×10−19 J. This tiny energy, about 2.48 eV, is typical of a single visible photon. The value 3.98×10−25 J is wrong because it drops six powers of ten by mishandling the wavelength conversion from nanometres. The value 6.63×10−34 J is wrong because it simply quotes Planck's constant without completing the calculation. The value 2.48×10−18 J is wrong because it is off by a factor of ten, likely from an arithmetic slip in the exponent. As stated in NCERT Class 12, Chapter 11, photon energy is inversely proportional to wavelength, so shorter wavelengths carry more energetic photons. It is worth stressing that this energy is an intrinsic property of a single quantum: doubling the beam power delivers twice as many such photons but never changes the energy each one carries. Expressed in electron-volts, the value 2.48 eV lies squarely in the visible range, which is why 500 nm light appears green to the eye and can readily excite molecular transitions in the retina. A magnitude check confirms that visible-light photons carry energies of order 10−19 J, matching the computed result.
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About This Question
- Subject
- physics
- Chapter
- dual nature of matter and radiation
- Topic
- photon energy
- Difficulty
- Medium
- Year
- 2025
Solution
Correct Answer:
Approximately 3.98 × 10⁻¹⁹ J
Each photon carries energy given in NCERT by E=λhc, where h=6.63×10−34 J·s is Planck's constant, c=3×108 m/s is the speed of light, and λ is the wavelength. Substituting λ=500×10−9 m gives E=500×10−9(6.63×10−34)(3×108)=5×10−71.989×10−25=3.98×10−19 J. This tiny energy, about 2.48 eV, is typical of a single visible photon. The value 3.98×10−25 J is wrong because it drops six powers of ten by mishandling the wavelength conversion from nanometres. The value 6.63×10−34 J is wrong because it simply quotes Planck's constant without completing the calculation. The value 2.48×10−18 J is wrong because it is off by a factor of ten, likely from an arithmetic slip in the exponent. As stated in NCERT Class 12, Chapter 11, photon energy is inversely proportional to wavelength, so shorter wavelengths carry more energetic photons. It is worth stressing that this energy is an intrinsic property of a single quantum: doubling the beam power delivers twice as many such photons but never changes the energy each one carries. Expressed in electron-volts, the value 2.48 eV lies squarely in the visible range, which is why 500 nm light appears green to the eye and can readily excite molecular transitions in the retina. A magnitude check confirms that visible-light photons carry energies of order 10−19 J, matching the computed result.
This medium difficulty physics question is from the chapter dual nature of matter and radiation, covering the topic of photon energy. It appeared in the 2025 exam.
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