Focus 1B #7B and 7C confusion

[Narhayne Nacana 3B]

The questions asks:

"Sodium vapor lamps, used for public lighting, emit yellow light of wavelength 589 nm. How much energy is emitted by
(a) an excited sodium atom when it generates a photon;
(b) 5.00 mg of sodium atoms emitting light at this wavelength;
(c) 1.00 mol of sodium atoms emitting light at this wavelength?"

For a, I know we have to use the E=h*v, but when I tried it it didn't work until I tried to use the E=h*(c/frequency). I was wondering when do we use either equation?

For b and c, I know it has to do something with moles and molarity because they give you mass and mol but I'm having trouble connecting it to finding the amount of energy? How does moles connect with energy here?

If anyone can explain these, any help will be appreciated!

[Shria G 2D]

Hi,

For part a, the equation is actually E = h(c/wavelength), not E = h(c/frequency). It comes from the equation E = hv and c = wavelength(v). The v in E = hv is substituted for c/wavelength from the second equation. Therefore, the equation is E = h(c/wavelength). You would use this equation when they give you wavelength like they did in this question. You would use E = hv when the problem gives frequency.

Also, the answer to part a is the energy emitted by 1 sodium atom and part c is asking for the energy emitted by 1 mol of sodium atoms. So, you need to convert the 1 atom to 1 mole. You know that there are 6.02 x 10^23 atoms in a mol so you can convert the energy per atom to the energy per mol by multiplying it by (6.02 x 10^23 atoms/mol).

For part b, they are asking for the energy emitted by 5 mg of sodium atoms so you can once again convert it by multiplying the energy per mol (from part c) by (1 mol / 22.98 g) which is the molar mass of sodium. This gives you the energy emitted by 1 g of sodium atoms. To find the energy emitted by 5 mg, you can multiply it by 0.005 g (5 mg converted to g).

I hope that helped!

[405513470]

Could you elaborate what you do after you get grams of sodium for part b?

[Shria G 2D]

So we need to find the energy emitted by 5.00 mg of sodium (or 0.005 g Na). In part a, we found the energy emitted by 1 atom of sodium so we want to find the energy emitted by 1 g of sodium because we can multiply that by 0.005 g to get the energy emitted by 0.005 g of sodium.

To do this, we could do (3.37 x 10^-19 J / 1 atom)(6.02 x 10^23 atoms / 1 mol)(1 mol / 22.99 g Na) which equals 8.83 x 10^3 J/g. This is the energy emitted per gram of sodium so to find the energy emitted by 0.005 g, we would multiply 8.83 x 10^3 * 0.005 which equals 44.1 J, which is the final answer.

So basically, you just have to convert the energy per atom to energy per gram and you can do so because we know 6.02 x 10^23 atoms = 1 mol and 1 mol Na = 22.99 g Na.

I hope that helps!