Wavelength of Photons: 3-2 Transition

[VanessaN]

Homework Statement

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

Homework Equations

[PLAIN]http://upload.wikimedia.org/math/0/e/f/0ef5602ad67cd5ef919e2ead1a173040.png,

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.

The Attempt at a Solution

[/B]

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?

 

[Borek]

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?

 

[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 :(

 

[Borek]

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.

 

[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 numbers3.01 * 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

 

[Borek]

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.

 

[my2cts]

Between which energy levels of what ?

 

[VanessaN]

Between which energy levels of what ?

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

 

[vela]

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