Homework Ch. 1 Question 25; 6th Edition

VGonzalez
Posts: 30
Joined: Fri Sep 28, 2018 12:18 am

Homework Ch. 1 Question 25; 6th Edition

In a previous posting from some time ago students said to answer parts b and c by multiplying the energy received in part a by the amount of atoms you get from the given masses. Why is this allowed? How do we know that multiplying the number of atoms by the energy will give the correct new energy?

Chem_Mod
Posts: 17528
Joined: Thu Aug 04, 2011 1:53 pm
Has upvoted: 393 times

Re: Homework Ch. 1 Question 25; 6th Edition

Please post the question as well.

Xingzheng Sun 2K
Posts: 62
Joined: Fri Sep 28, 2018 12:29 am

Re: Homework Ch. 1 Question 25; 6th Edition

The question is:
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?

Mindy Kim 4C
Posts: 65
Joined: Fri Sep 28, 2018 12:25 am

Re: Homework Ch. 1 Question 25; 6th Edition

For part b, you can find the number of sodium atoms in 5.00 mg of sodium by doing the following:
(5.00 mg Na)(1 g Na/1000 mg Na)(1 mol Na/22.99 g Na)(6.022x10^23 atoms/1 mol Na) = 1.3097 x 10^20 atoms Na
(1.3097x10^20 atoms)(3.37x10^-19 J/atom)=44.1 J

The reason why you multiply the energy from part A by the number of atoms is because the energy from part A is the energy emitted per Na atom. Therefore, to get the energy emitted by all the atoms in 5.00 mg of sodium, you would need to multiply the energy per atom by the number of atoms.

For part c, the same applies but this time you have 1.00 mol of Na atoms. Therefore, there are 6.022x10^23 atoms of Na. You multiply the energy per atom from part a by Avogadro's number to get 2.03x10^5 J.

Sophia Ding 1B
Posts: 62
Joined: Fri Sep 28, 2018 12:16 am

Re: Homework Ch. 1 Question 25; 6th Edition

If it helps, you can think about it in terms of units to see how it works out! The answer from part A is energy given in joules/atom:

For part b, once you convert mg of Na atoms to number of Na atoms, you can multiply the energy answer from part a with the atoms you have calculated to just get overall energy in joules, as the question desires.

You can similarly do the same thing with part c; once you convert the moles of Na atoms to number of Na atoms using Avogadro's number, you are left with the units of atoms. Multiplying that by the energy from part a, the units of J/atoms * atoms cancels out to leave just joules of energy, which is what you are looking for!