Calculate energy of half mole of photons of a radiation with frequency \(3 \times 10^{12} \mathrm{~Hz}\).

Calculate energy of half mole of photons of a radiation with frequency \(3 \times 10^{12} \mathrm{~Hz}\).
  1. \(598.2 \mathrm{~kJ} \mathrm{~mol}^{-1}\)
  2. \(0.598 \mathrm{~kJ} \mathrm{~mol}^{-1}\)
  3. \(1.196 \mathrm{~kJ} \mathrm{~mol}^{-1}\)
  4. \(119.6 \mathrm{~kJ} \mathrm{~mol}^{-1}\)

Solution

Energy of a photon, \(E=h v\), where, \(v=\) frequency \(=3 \times 10^{12} \mathrm{~Hz}\) Therefore, energy \(=6.6 \times 10^{-34} \times 3 \times 10^{12} \mathrm{~Hz}=1.9878 \times 10^{-21} \mathrm{~J}\) 1 mole \(=6.02 \times 10^{23}\) photons, therefore, \(\frac{1}{2}\) mole \(=3.01 \times 10^{23}\) photons Therefore, energy of \(\frac{1}{2}\) mole of photons \(\begin{aligned} & =1.9878 \times 10^{-21} \times 3.01 \times 10^{23} \\ & =0.5982 \mathrm{~kJ} / \mathrm{mol} \end{aligned}\) Hence, the correct option is (b).

Asked in: AP EAMCET 2020 (21 Sep Shift 2)

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