JEE Main 2023 · 30 January · morning · Numerical answer · +4 / −0

The energy of one mole of photons of radiation of frequency 2 × 10¹² Hz in J mol⁻¹ is ___________. (Nearest integer)
[Given : h=6.626 × 10⁻³⁴ Js
N_A=6.022 × 10²³ mol⁻¹]

Answer and solution

Answer 798

Solution

Chemistry ma’am · 3 steps

Find the energy of one photon with E = hν, then multiply by Avogadro's number for a whole mole.

  1. One photon. Planck's relation gives the energy of a single photon: E = hν = 6.626 × 10⁻³⁴ × 2 × 10¹² = 1.3252 × 10⁻²¹ J.

    Eₘₒₗₑ = N_A hν

  2. One mole. A mole contains 6.022 × 10²³ photons, so Eₘₒₗₑ = 6.022 × 10²³ × 1.3252 × 10⁻²¹ = 798.04 J mol⁻¹.
  3. So. The energy of one mole of photons is about 798.04 J mol⁻¹, which rounds to 798.

The idea to keep. Whenever a question says "one mole of photons", find hν for one photon first, then multiply by N_A. Watch the units the answer asks for, J or kJ.

Answer from the NTA final answer key. Solution by PrepWiser.

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Asked about 170 times in JEE Main since 2020. This question is from 2023.