## Homework 1.25b

Neha Divi 1K
Posts: 31
Joined: Fri Apr 06, 2018 11:02 am

### Homework 1.25b

1.25 Sodium vapor lamps, used for public lighting, emit yellow light of wavelength 589 nm. How much energy is emitted by
(b) 5.00 mg of sodium atoms emitting light at this wavelength;

Hi, I was slightly confused on following the steps for part b. I was wondering if someone could explain them more thoroughly for me.

Anna De Schutter - 1A
Posts: 66
Joined: Wed Feb 21, 2018 3:01 am

### Re: Homework 1.25b

Hi!

So when we did question 1.25 a, we found that the energy emitted with one sodium atom is 3.37*10^-19J. In this question we are asking how much energy is emitted with 5.00mg of those sodium atoms.

To solve this problem, we need to find how many sodium atoms there are in 5.00mg so that we can multiply 3.37*10^-19J by that number.

We are thus going to use the equation: N=n*Na
We now have the mass of sodium atoms, let's first convert it to moles by using the molar mass: (5.00*10^-3g Na)/(22.99g Na/mol Na).
We can then find the number of atoms in 5.00mg of sodium atoms by multiplying it by Avogadro's constant: N=n*Na=(5.00*10^-3g Na)/(22.99g Na/mol Na)*(6.022*10^23 atoms Na/mol Na).

We have now found the number of atoms in 5.00mg of sodium.

Because 3.37*10^-19J is emitted with one sodium atom, we multiply 3.37*10^-19J by (5.00*10^-3g Na)/(22.99g Na/mol Na)*(6.022*10^23 atoms Na/mol Na) to get the amount of energy emitted with 5.00mg of sodium atoms.

This gives us:
(5.00*10^-3g Na)/(22.99g Na/mol Na)*(6.022*10^23 atoms Na/mol Na)*(3.37*10^-19J/ Na atoms)=44.1J
And this is the answer given in the solutions manual.

I hope this helps! :)
Anna De Schutter - section 1A