Question

The latent heat of fusion of ice is $330{\text{J g}}^{-1}$. Calculate the number of photons of radiation of frequency $5\times {10}^{13}{\text{s}}^{-1}$ to cause the melting of 1 mole of ice. Take $h=6.6\times {10}^{-34}\text{J s}$. Express your answer as $X\times {10}^{23}$, what is the value of $X$?

Answer 1

Heat required for melting 1 mole (18 g) of ice $=330\times 18=5940\text{J}$
Energy of one phton $=hv$
$=6.6\times {10}^{-34}\times 5\times {10}^{13}=33\times {10}^{-21}\text{J}$
Total number of photons required $=\frac{5940\text{J}}{33\times {10}^{-21}\text{J}}=18\times {10}^{22}$
$=1.8\times {10}^{23}$
$\therefore X=1.8$