Question

The dissociation energy of $H _{2}$ is $103 \cdot 2 kcal mol ^{-1}$. A hydrogen molecule is irradiated with a photon of wavelength 2537 Å. Suppose this photon is completely absorbed by one molecule of $H _{2}$ resulting into dissociation. Calculate how much photon energy is converted into kinetic energy imparted to atoms.

Answer 1

SOLUTION : Energy of the photon of wavelength 2537Å

$=\frac{h c}{\lambda}=\frac{6.626 \times 10^{-34} J_{. s .} ms ^{-1} \times 3 \times 10^{8}}{2537 \times 10^{-10} m } J =7.835 \times 10^{-19} J$

Energy for dissociation of $H _{2}$ molecule

$=\frac{103 \cdot 2 \times 10^{3} \times 4 \cdot 18}{6 \cdot 02 \times 10^{23}} J =7 \cdot 165 \times 10^{-19} J$

Excess energy that is converted into kinetic energy

$=(7 \cdot 835-7 \cdot 165) \times 10^{-19}=6 \cdot 7 \times 10^{-20} J \text {. }$