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There is a question, that says:
What total energy (in $\mathrm{kJ}$) is contained in $1.0~\mathrm{mol}$ of photons, all with a frequency of $2.75 \cdot 10^{14}~\mathrm{Hz}$?
My answer was:
The energy of photon in hydrogen atom is given by the formula $E=h\nu$, where $h$ is Planck constant and $\nu$ is the frequency. After that I got an answer different from the correct answer which is $110~\mathrm{kJ}$.
Could anyone explain why?
The formula $E=h\nu$ is for the energy of one photon. You have a mole of photons. You need to use a slightly modified form:
$$E=Nh\nu$$
where $N$ is the number of photons, in this case
$$\begin{align} N&=n\cdot N_\mathrm A\\[6pt] &=1\ \mathrm{mol}\times6.02\times10^{23}\ \mathrm{mol^{-1}}\\[6pt] &=6.02\times10^{23} \end{align}$$
Note that you are being asked to report energy in kilojoules not kilojoules per mole.
If I use $E=nN_\mathrm A h \nu$, I get the correct answer you cite of $110~\mathrm{kJ}$. Do you?
