## Textbook problem 1B 7?

$E=hv$

Megan Hulsy 1A
Posts: 119
Joined: Wed Sep 30, 2020 9:51 pm

### Textbook problem 1B 7?

hi!

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?

I don't understand how to do this problem, thanks!

Audra Mcleod 3G
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### Re: Textbook problem 1B 7?

Hello!
a) So to determine the energy of an excited sodium atom, you would first use the wavelength to determine the frequency of the light emitted through the equation speed of light =(wavelength)(frequency). This would give you 5.093 x 10^14 (3.0x10^8/589x10^-9). You would then use this frequency in the equation E = hv, which would give you a final answer of 3.37 x 10^-19 J (6.626x10^-34 x 5.093x10^14).
b) For the energy of 5.00 mg, you would have to convert this value to the number of sodium atoms, and multiply by the energy per atom you calculated in a). This conversion would look like this:
5 mg/1 x 1 g/ 1000 mg x 1 mol/ 22.99 g x 6.022x10^23 atoms/ 1 mol = 1.3097 x 10^20 atoms x 3.37x10^-19 = 44.1 J
c) For this problem, it is the same method in b), except you don't have to convert to number of atoms because you already know there is 6.022x10^23 atoms in 1 mole. So you would simply do (6.022x10^23)(3.37x106-19)= 202,941.4 J, but since the numbers given in the problem only has 3 sig figs you would round this number to 203,000 J or 203 kj.
Hope this helps!

Nane Onanyan 1G
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Joined: Wed Sep 30, 2020 9:43 pm
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### Re: Textbook problem 1B 7?

Hi!
For a, you would need E=hc/lamda
Just plug in the variables and solve for E! (Remember to convert nanometers to meters for wavelength)
Once you find the amount of energy for ONE sodium atom, you could use this for part b.

For b, you first need to convert 5mg of Na to g. From part A, we know that one sodium atom emits X joules of energy. We can use this as a proportion to solve for b.
Convert 5mg of Na to atoms. Then multiply the number of Na atoms by the answer to part a.
X g Na * (1mol Na/22.99g Na) * (6.022*10^23 atoms/1mol Na) * (X J/1 atom Na)= energy emitted by 5mg of Na

It is the same process for C except you have to convert moles to grams first.

I am sorry I did not have time for calculations, so I just replaced them with X. I hope this helps you get the idea though!
edit: Someone also answered this at the same time (oops) but I will keep this here just in case.

Megan Hulsy 1A
Posts: 119
Joined: Wed Sep 30, 2020 9:51 pm

Thank you!! :)