The energy of one mole of photons of radiation of frequency $2 \times 10^{12} \mathrm{~Hz}$ in $\mathrm{J} \mathrm{~mol}^{-1}$ is ______. (Nearest integer) (Given: $\mathrm{h}=6.626 \times 10^{-34} \mathrm{Js}$ $\mathrm{N}_{\mathrm{A}}=6.022 \times 10^{23} \mathrm{~mol}^{-1}$)

JEE Main · 2023 · 30 Jan 2023 · Shift 1 · Atomic Structure

The energy of one mole of photons of radiation of frequency

2 \times 1 0^{12} Hz

J mol^{- 1}

is ______.
(Nearest integer)
(Given:

h = 6.626 \times 1 0^{- 34} Js

N_{A} = 6.022 \times 1 0^{23} mol^{- 1}

)

Answer: 798

The energy of one photon is

E = h ν

, so for a mole of photons

E = N_{A} h ν

. Substituting,

E = 6.022 \times 1 0^{23} \times 6.626 \times 1 0^{- 34} \times 2 \times 1 0^{12}

. Collecting the powers of ten gives

79.8 \times 1 0^{1}

, that is

798 J mo l^{- 1}

JEE Main · 2023 · 30 Jan 2023 · Shift 1 · Integer answer