# What total energy (in kJ) is contained in 1.0 mol of photons, all with a frequency of 2.75 • 10¹⁴ Hz?

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 $2.75 \cdot 10^{14}~\mathrm{Hz}$?

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?

• what values did you use in the equation? – ron Jul 2 '14 at 17:40
• $2.75 \times 10^{14}$ x 6.63e-34 = 1.82e-19 KJ ?? – Maher Jul 2 '14 at 17:46
• I get the same answer as you, except your answer is in J/mol, you need to divide by 1000 to convert it to kJ/m – ron Jul 2 '14 at 17:56
• I did, but still far away from the right answer ! – Maher Jul 2 '14 at 18:00

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?

• Yes I do ! but I didn't know that avogadro number is used to convert mol to photons .. I know that it is used to convert mol to atoms or molecules.. thanks ! – Maher Jul 3 '14 at 11:44
• The units on Avogadro's number are $\text{mol}^{-1}$, so you can convert between number of anything and moles of anything. A mole is just a counting aid for very large numbers of things. – Ben Norris Dec 3 '14 at 11:40