Midterm Question 4

[Julia Mazzucato 4D]

Hi, this was one of the questions I messed up on on the midterm. I'm redoing the entire test right now to study for the final and I'd love if someone can check my answer for question 4.

Question: Light with wavelength 102.557 nm excites a hydrogen atom gas sample. Is the change in energy of a hydrogen atom positive or negative when it absorbs a photon? What is the principal quantum number of the state the electron was excited to?

If 100kJ of energy was absorbed by the gas sample, how many photons in total caused electronic excitations? How many moles of hydrogen were excited assuming one photon interacted with one unique hydrogen atom?

For the first part, I got my E_change to be 1.938 x 10^-19 J using E=hc/lambda. This value is positive, but looking at the values I got for E_initial and E_final the final E is smaller, so would that mean the change in energy is negative?
For my quantum # I got n=3

For the second part, I got 5.16 X 10²² photons and 0.0857 moles of H.

[Prasanna Padmanabham 4I]

Those are the same answers I got (and I got the answer correctly). En= Eupper - Elower, but En= - hR/n^2, so when you plug it in you would get: En = -Eupper - (-E lower) so En=-Eupper + Elower. Since as n increases, En get closer to 0, and as n gets smaller, En decreases (remember big negative number).

So, just be mindful of the signs and you will see that the En is positive if the electron goes from a small n shell to a higher shell.