Question

What will be the energy of 1 mole of photons having a wavelength of 200 nm?
Planck’s constant, \( h = 6.6 \times 10^{-34} \, \mathrm{Js} \) and Speed of light, \( c = 3.0 \times 10^8 \, \mathrm{ms^{-1}} \)

• A. \(-19.8 \times 10^{-19} \, \mathrm{KJ \, mol^{-1}}\)
• B. \(\sim 9.9 \times 10^{-19} \, \mathrm{KJ \, mol^{-1}}\)
• C. \(-599 \, \mathrm{KJ \, mol^{-1}}\)
• D. \(\sim 599 \, \mathrm{J \, mol^{-1}}\)

Hint:

Always ensure that the wavelength is converted to meters (λ = 200nm = 200×10^−9m) before performing calculations.

Answer 1

The Correct Option is C

1. Calculate the energy of one photon:

\( E = \frac{hc}{\lambda} \)

Substituting the values:

\[ E = \frac{6.6 \times 10^{-34} \times 3.0 \times 10^{8}}{200 \times 10^{-9}} \]

\( E = 9.9 \times 10^{-19} \, \text{J} \)

2. Calculate the energy of 1 mole of photons:

\( E_{\text{mole}} = E \times N_A \)

\[ E_{\text{mole}} = 9.9 \times 10^{-19} \times 6.022 \times 10^{23} \]

\( E_{\text{mole}} = 5.96 \times 10^{5} \, \text{J mol}^{-1} \)

3. Convert to kilojoules:

\( E_{\text{mole}} = 599 \, \text{kJ mol}^{-1} \)