Solving Unexplained Homework Question: Sodium Emission Line at 589nm

[Sephiroth2088]

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.

 

[Hootenanny]

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?

 

[kyle8921]

Hello there,

I understand your confusion about this homework question. Let me explain the steps to solve it.

Firstly, we need to know the formula for calculating energy (in joules) of a photon emitted by an atom. It is given by E = hc/λ, where h is Planck's constant (6.626*10^-34 J*s) and c is the speed of light (3*10^8 m/s).

Next, we need to convert the wavelength from nanometers (nm) to meters (m) as the formula uses meters. This can be done by dividing the wavelength (589 nm) by 10^9. This gives us a value of 5.89*10^-7 m.

Now, we can plug in the values in the formula to get the energy of a single photon emitted by sodium atoms at 589 nm. This comes out to be 3.37*10^-19 J.

Since we are given the number of moles of excited sodium atoms (0.2698 moles), we need to multiply the energy of a single photon by Avogadro's number (6.022*10^23) to get the total energy produced by all the excited atoms.

Therefore, the final calculation would be 0.2698*6.022*10^23*3.37*10^-19 J, which gives us 5.481*10^4 J.

I hope this helps you understand the process of solving this question. If you have any further questions, please feel free to ask. Good luck with your homework!