# Wavelength of photons

1. May 21, 2015

### VanessaN

1. The problem statement, all variables and given/known data

Between which energy levels are the photons in this line transitioning?

Wavelength= 660 * 10^-9 m
Change in energy = 3.01 * 10^-9

A. 4 and 2
B. 3 and 2
C. 3 and 1
D. 2 and 1

2. Relevant equations

E is energy, h is Planck's constant (6.63 x 10-34 J s), f is frequency, c is the speed of light (3.00* 10^8 m/s), and λ is wavelength.

3. The attempt at a solution

Ok, so I could solve for frequency using either of these equations with the given info, but how would that help me determine which energy levels the photons are transitioning from?

Answer: The photon with the lowest energy and longest wavelength corresponds to the 3 to 2 transition.
(there were 3 other lines of given data, the line in this question was the lowest energy and longest wavelength)
How can you tell that the photon with the lowest energy and longest wavelength corresponds to the 3 to 2 transition?

Last edited by a moderator: May 7, 2017
2. May 21, 2015

### Staff: Mentor

Hint: none of the equations you listed is the one you need.

Do you know of any equation that uses energy level numbers (principal quantum numbers) to calculate wavelength (or frequency) of the photon?

3. May 21, 2015

### VanessaN

E= - Rh/ n^2,

where E is the energy of the electron and Rh is the Rydberg constant (2.18 * 10^-18)

3.01 * 10^-9= -(2.18 * 10^-18)/ n^2
n^2= 7.24 * 10^-10
n= 2.69 * 10^-5

I don't really know of other equations to use :(

4. May 21, 2015

### Staff: Mentor

Rydberg is a correct name, but the formula you have used is not the one you need (although it is a specific version of the correct one). Please recheck your notes or book. Or visit wikipedia.

5. May 21, 2015

### VanessaN

Thank you. maybe this equation:
Energy of electron transition= -Rh ( 1/ ni^2 - 1/ nf^2)
where ni and nf are the intial and final principal quantum numbers

3.01 * 10^-9= -(2.18 * 10^-18) * (1/ ni^2 - 1/ nf^2)

3.01 * 10^-9= -(2.18 * 10^-18) * (1/ 3^2 - 1/ nf^2)

3.01 * 10^-9= -(2.18 * 10^-18) * (1/ 9 - 1/ nf^2)

-7.24 * 10^-10= (1/ 9 - 1/ nf^2)

-7.24 * 10^-10= 1/ 9 - 1/ nf^2

-6.52 * 10^-9= - 1/ nf^2

153414882.8= nf^2

nf= 12386

Last edited: May 21, 2015
6. May 21, 2015

### Staff: Mentor

Yes, Rydberg formula is definitely the one to use.

The result you got is wrong, which is rather obvious - the answer should be a small integer. It is hard to say what went wrong, my bet is that you have use incorrect units. Hard to tell not seeing them, please always list units in your calculations, as they are a key to getting a correct answer.

7. May 21, 2015

### my2cts

Between which energy levels of what ?

8. May 21, 2015

### VanessaN

Energy levels of an electron... I was just copying down the question :)

9. May 26, 2015

### vela

Staff Emeritus
The energy you calculated (I'm assuming it's in units of joules) is $10^{10}$ times too large.