Problem on the wavelength of the electromagnetic radiation needed to break 1 mol of gas [closed]








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**Problem.**
To break the bonds in 1 mol of Cl$\_2$ we need E=243.4 kJ of energy. The bonds on this amount of gas can be broken by electromagnetic radiation of a certain length. Determine the wavelength.


**Solution.**
Firstly, there are 34 electrons in the molecule Cl$\_2$. So in 1 mol of Cl$\_2$, there are $n\_e = 34\cdot N\_A = 2.05\times 10^{25}$ electrons, where $N\_A=6.022\times 10^{23}$ mol$^{-1}$ is Avogadro's constant. Now, the amount of energy needed for a single electron is (on average) $E\_e = E/n\_e = 1.19 \times 10^{-20}$ J.


We know that energy is related to the wavelength $\lambda$ by the relation
$$
E\_e = h\frac{c}{\lambda},
$$
where $h=6.63\times 10^{-34}\, m^2 kg/s$ is the Planck constant and $c=3.00\times 10^8 \,m/s$ is the speed of light in vacuum. Thus


$$
\lambda = \frac{hc}{E\_e} = 169\,nm.
$$
[Solution provided: 492 nm]


Am I doing something wrong?


**UPDATE**
I got the mistake thanks to @Domen (+10). I don't have to count all electrons but only those involved in the bonding. There is a single pair of electrons to be broken in a single chlorine molecule. In 1 mole of chlorine there are $N\_A$ bonds, thus $n\_e = N\_A$. So the correct answer is $\lambda = 492$ nm.


