HW Question 1.25

[Danah Albaaj 1I]

Question #25 states:
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 used Einstein's E=hv and v=c/lambda to determine the energy of the photon. However, my answer was 3.37 x 10^-15 which did not match the solution given. I converted the wavelength into meters and cannot see where I went wrong. Please help!

Also, what steps am I supposed to take to complete the rest of this question?

[Victoria Draper 1G]

Hi!

So for part a instead of finding energy using two separate equations, you can combine the two equations as E=hc/lambda which would be the same thing as solving for v first and then plugging it into the E=hv equation. The problem initially gives you the wavelength in nanometers so be sure to convert the 589 nm to (589 x 10^-9)m. When using the combined equation, the setup for the problem would be E= (6.626 x 10^-34)(3.00 x 10^8)/(589 x 10^-9) which should give you 3.37 x 10^-19 J.

For part b, you have to convert the amount of Na they give you from grams to moles and from moles to atoms. Once you get a number for the amount of atoms, you multiply it by the amount of energy that you found in part a which was 3.37 x 10^-19. The product of the amount of atoms and the energy will be your final answer for this part.

For part c, you must convert from moles to atoms and then, just as in part b, multiply it by the energy that you found in part a.

Hopefully this helps!

[Cade Okohira 4K]

First you need to convert the wavelength to energy, which you can do my manipulating the two formulas E=hv and c=v(wavelength) to get E=hc/wavelength. I found this to be 3.375x10^-19 J. For part b, I converted mg into mol and then into atoms. Then, I multiplied this amount by the answer I found in part a because that is the energy for one atom. For c, I just had to multiply the amount by Avogadro's number and then by the energy of one sodium atom.