1B #7 part b

[Minahil_Tufail_3I]

Hi, I'm confused on how to solve part b for this question and would appreciate some help with it:
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?
Thank you!

[Bronson Mathos 1H]

In part B, you are asked to calculate the amount of energy emitted by 5.00mg of sodium at the given wavelength, and in order to do this, you simply convert the 5.00mg of sodium to moles(you must first convert mg to g) and then to particles and then multiply this result by the energy emitted from a single sodium atom(found in part A(3.37*10^-19J). So the numerical form of this is: 0.05gNa*(1molNa/22.99gNa)*(6.022*10^23atoms*mol^-1)*(3.37*10^-19J*atom^-1)=44.1J

[Anil Chaganti 3L]

Hi, you need to convert mg to atoms using Avogadro's and then use your answer from part a (using E=hc/wavelength). Then, multiply the number of Na atoms and the energy to get the energy emitted by Na specifically.

[Leo Naylor 2F]

In order to get part b, we first need to solve part a. If sodium emits light of a wavelength of 589 nanometers, we can divide the speed of light (3*10^8 m/s) by 589 nanometers (5.89 * 10^-7) to find the frequency, 5.09 * 10^14 Hz. We can multiply this number by Planck's constant to find the energy emitted by a single atom of sodium. 5.09 * 10^14 times 6.626 * 10^-34 equals 3.37 * 10^-19 J. For part b, we need to find the number of sodium atoms in 5 milligrams. The molar mass of sodium is 22.99 grams, so we can divide 0.005 by this number to find how many moles of sodium are in 5 milligrams. The answer is .000217 moles. Next, we can multiply .000217 moles by Avagadro's number (6.022 * 10^23) to find how many atoms of sodium are in 5 grams. There are 1.31 * 10^20 atoms of sodium in 5 milligrams. Finally, we multiply this number by the energy released per atom to find the answer. We get 44.1 J. Hope this helps!

[Crystal Pan 2G]

1. you take 5.00 mg and get grams of Na
2. divide by the molar mass of Na (22.99)
3. multiply by avogadro's number to get amount of Na atoms in 1 mole of Na
4. multiply by the energy you got in answer a

hope that helped!

[Kiyoka Kim 3C]

Part (a) gives you the energy for 1 sodium atom. In part (b) you are asked to find the energy emitted by 5.00mg of sodium atoms. So you first have to find the number of sodium atoms there are in 5.00mg by using Avogadro's constant. Then you can multiply the number of sodium atoms in 5.00mg you found with the answer for part (a).