CHEMISTRY COMMUNITY

Sodium vapor lamps emit yellow light of wavelength 589 nm. How much energy is emitted by b) 5.00mg of Na atoms emitting light at this wavelength?

From a) I found that the energy emitted by an excited sodium atom is 3.37 x 10^-19 J. Then for part b, I found that 5.00mg of Na atoms = 1.31 x 10^20 Na atoms. The solutions manual says that you have to multiply 3.37 x 10^-19 J (and they list the unit as J/atom) with 1.31 x 10^20 Na atoms to get Joules in your ending answer. How come you can't just do (3.37 x 10^-19 J) / (1.31 x 10^20 atoms) to get J/atom as your answer instead of multiplying it together and getting Joules as your answer?

It wants to know how much energy is emitted from that quantity of sodium atoms so the answer would be the total amount of energy emitted by all of the atoms not per individual answer so J/atom would be incorrect since you that is not the energy per each atom.

In part a, you found the energy emitted by one atom of sodium which was 3.37x10^-19 J. Since there are 1.31^20 atoms in 5.00mg of Sodium, it emits 1.31x^20 times more energy than one Sodium atom alone. This is why you multiply instead of divide.