## Chapter 1 #55

H-Atom ($E_{n}=-\frac{hR}{n^{2}}$)

MichelleTran3I
Posts: 25
Joined: Fri Sep 29, 2017 7:06 am

### Chapter 1 #55

Infrared spectroscopy is an important tool for studying vibrations of molecules. Just as an atom can absorb a photon of suitable energy to move an electron from one electronic state to another, a molecule can absorb a photon of electromagnetic radiation in the infrared region to move from one vibrational energy level to another. In infrared spectroscopy, it is common to express energy in terms of /c, with the units cm 1 (read
as reciprocal centimeters). (a) If an absorption occurs in the infrared spectrum at 3600 cm 1, what is the frequency of radiation that corresponds to that absorption? (b) What is the energy, in joules (J), of that absorption? (c) How much energy would be absorbed by 1.00 mol of molecules absorbing at 3600 cm 1?

I was able to calculate frequency for part a, but how would you convert the energy to joules for part b?

Leon Popa
Posts: 18
Joined: Fri Sep 29, 2017 7:04 am

### Re: Chapter 1 #55

Hi Michelle,

For part b, I used the formula E = h*V, where h is planck's constant (6.626 * 10^-34 Js) and V is the frequency you calculated in part a. If you got V = 1.1 * 10^14 Hz as I did, then multiply that by planck's constant to get the energy in joules. Hz or Hertz, are the same thing as "per second" or s^-1.

So, looking at how the units cancel out:

E = (6.626 * 10^-34 Js)(1.1 * 10^14 s^-1)

E = 7.16 * 10^-20 J
or
E = 7.2 * 10^-20 J

Hope that helps,
- Leon.