Homework Ch. 1 Question 25; 6th Edition

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VGonzalez
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Homework Ch. 1 Question 25; 6th Edition

Postby VGonzalez » Mon Oct 15, 2018 1:18 pm

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

Postby Chem_Mod » Mon Oct 15, 2018 3:11 pm

Please post the question as well.

Xingzheng Sun 2K
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Re: Homework Ch. 1 Question 25; 6th Edition

Postby Xingzheng Sun 2K » Tue Oct 16, 2018 1:02 am

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

Postby Mindy Kim 4C » Tue Oct 16, 2018 9:02 am

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

Postby Sophia Ding 1B » Tue Oct 16, 2018 11:42 am

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!


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