Question

The energy of one mole of photons of radiation of frequency 2 \(\times\)10¹² H_z in Jmol^-1 is ________ (Nearest integer) 

[Given : \(h=6.626\times10^{-34}Js\)

 \(N_{A}=6.022\times10^{23}mol^{-1}\)]

Hint:

To calculate the energy of one mole of photons, first determine the energy of a single photon using E = hν. Then, multiply this by Avogadro’s number (NA) to find the energy for one mole.

Answer 1

Correct Answer: 798

Energy of One Photon
The energy of a single photon is given by:
\[E = h\nu,\]
where \(h = 6.626 \times 10^{-34}~\text{Js}\) and \(\nu = 2 \times 10^{12}~\text{Hz}\). Substitute the values:
\[E = 6.626 \times 10^{-34} \cdot 2 \times 10^{12} = 1.3252 \times 10^{-21}~\text{J}.\]
Step 2: Energy of One Mole of Photons
The energy of one mole of photons is:
\[E_{\text{mole}} = N_A \cdot E,\]
where \(N_A = 6.022 \times 10^{23}\). Substitute the values:
\[E_{\text{mole}} = 6.022 \times 10^{23} \cdot 1.3252 \times 10^{-21} = 798.16~\text{J}.\]
Approximate to the nearest integer:
\[E_{\text{mole}} \approx 798~\text{J mol}^{-1}.\]
Conclusion: The \textbf{energy} of one mole of photons is \(\mathbf{798~\text{J mol}^{-1}}\).