Question

Calculate energy of one mole of photons of radiation whose frequency is $5\times {10}^{14}{H}_Z$.

Answer 1

Given, $\text{frequency of photon}=5\times {10}^{14}{s}^{-1}$
Step 1 Energy of photon

We know that,
Energy $\left(E\right)$ of one photon is given by the expression $E=hv$
where,
$h\to \text{Planck's constant}=6.626\times {10}^{-34}Js$
$v\to \text{frequency}$

Step 2 Energy of one photon

Put values of $h$ and $v$ in above formula, we get:
$E=(6.626\times {10}^{-34}Js)\times (5\times {10}^{14}{s}^{-1})$
$=3.313\times {10}^{-19}J$

Step 3 Energy of one mole of photons

So, energy of one mole of photons will be:
$=(3,313\times {10}^{-19}J)\times N_A$
$=(3.313\times {10}^{-19}J)\times (6.022\times {10}^{23}mo{l}^{-1})$
$=199.51kJmo{l}^{-1}$
Final answer:$199.51kJmo{l}^{-1}$