Solving Unexplained Homework Question: Sodium Emission Line at 589nm

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To calculate the energy produced by 0.2698 moles of excited sodium atoms emitting light at 589 nm, first determine the energy of a single photon using the formula E = hc/λ, where h is Planck's constant and c is the speed of light. The energy of one photon at 589 nm is approximately 3.37 x 10^-19 joules. Next, calculate the total number of sodium atoms in 0.2698 moles, which is about 1.63 x 10^23 atoms. Assuming each atom emits one photon, multiply the energy of a single photon by the total number of photons to find the total energy, resulting in approximately 5.481 x 10^4 joules. This method effectively links the concepts of moles, photons, and energy in quantum mechanics.
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Hello, I'm new and I have a question about something on my homework that I just can't find an explanation how to do.

if sodium has an emmsion line at 589nm, what is the energy (in joules) produced by 0.2698 moles of excited sodium atoms?

The answer is apparently 5.481*10^4

If anyone could tell me how to go from those above numbers to that answer I would sure appreicate it, thanks in advance.
 
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Some questions to think about;
  1. What is the energy of a single photon with a wavelength of 589nm?
  2. How many sodium atoms in a mole of sodium?
  3. How many sodium atoms in 0.2698 moles of soduim?
  4. Assuming each of the atoms is excited to the same level, how many 589nm photons are produced?
 

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