Chemistry Question - Light

Alright, so here's the problem.

"If a helium atom absorbs a photon with a wavelength of 58.44 nm, one electron will be promoted from the 1s orbital to the 2p orbital.

A) Find the energy, in J, gained by a helium atom undergoing this transition."

First part's easy. E = hc/wavelength. The answer in the answer key is 3.399 x 10^-19, but I'm only getting 3.4 x 10^-18. Could it be a typo or am I doing something wrong:

E = [(6.626*10^-34 Js)(3*10^8 m)]/(58.44*10^-9 m).

However, B) is confusing me.

"The ionization energy of helium is 2372 kJ/mol. Suppose that a helium atom has already undergone the transition above, so that it has one electron in a 2p level. What is the longest wavelength of light that would be capable of supplying enough energy to eject an electron from this excited helium atom, producing a He+ ion?"

I'm assuming I'm going to have to use my result from part A, as well as the ionization energy that they gave me, but I have no idea what to do with them. Any advice?

In A, Plank's constant (h) is 6.526 x 10^-34, not -24. You converted nanometers to meters right. The rest is set up right.

When I do it I get 3.39 x 10^ -18... I'm sure that's what you meant when you said 3.4 x 19^-18

In B...Ionization energy is the energy an electron takes to break away from an atom.

They're saying is takes 2372 kJ (AKA 2372000 J) to break away completely from the first energy level. But since your electron is starting at the 2p level, you can subtract your previous answer (3.4 x 10^-18 J) from 2372000 J's total (which is basically the same 2372000 J) and then solve your equation. Except this time instead of not knowing energy and knowing wavelenth, you don't know wavelength and you do know energy.

 What I got when solving for B

8.38 x 10^-32 meters

I'm on Spring Break so my mind is off, but this is kind of how to do it I guess. If it doesn't work, just post so and I'll go look for a book or something to brush up on this stuff.

Yeah, just dumb typos because it was late when I posted the question.

And I probably should have posted the answer whenever I wrote the thread. Part B) is supposedly 3.68X10^-7 m, but looking through the notes I was able to find an example like it. Hurr durr.

I guess the answer from part A) is in J/mol, not just J, so you convert the energy into J for one atom, then solve for wavelength from the E = hc/lambda. Okay I have no idea, lol. When I did this, I didn't get 3.68E-7, but some other number. Then converting the ionization energy into J/atom and solving for lambda didn't work either, so I'm thoroughly confused.

Ohhhhhhhhhhhhhhhhhhhhhhhhhhh I didn't notice the atom/mole thing...

Okay first of all convert Energy to J/atom.

So 2372 kJ/mol = 3272000 J/mol.
To convert to J/atom divide by Avogadro's number (6.022E23)

So the total energy for an electron to leave an atom of Helium is 3.93E-18.

Since it's already in the second energy level (2p) we subtract our 3.4E-18 from 3.95E-18, and get that it needs 5.388E-19 Joules of energy more for the electron to get out of the Helium.

Plug that number into your formula E=hc/wavelength and you should get the same answer in the book, 3.68E-7 meters.

And in hindsight, since we used the number from A in question B, and it worked out perfectly to get the answer in B, then our answer to question A was right and your book has a typo.

You are awesome, sir. And I was just about to leave to ask my professor, too.

Have my second exam for the class today, and with your help I think I'll be able to pull off an A now.

Gl on that exam floe .