What is the wavelength of the emitted light in the infinite well problem?

[Kawakaze]

Homework Statement

The mass of the particle in the infinite well is 2.00 × 10−30 kg, and the width of the well is 1.00 × 10−9 m. If the particle makes a transition from the third eigenstate to the second eigenstate, what will be the wavelength of the emitted light?

Homework Equations

E(emitted) = E(3) - E(2)

E(3) = 9h^2/8mD^2
E(2) = 4h^2/8mD^2

E(photon) = hc/lambda

The Attempt at a Solution

I thought this would require solution using the equations above and then use the energy found to calculate the photons wavelength. The only problem is I get weird units after working out the energy of the photon. I get the SI units to be J^2 s^2 kg^-1 m^-2. I would expect the units to cancel to just J. They don't so I assume I am going wrong somewhere, is my approach correct? =S

 

[kuruman]

The approach is correct. Can you do dimensional analysis on the equation you have posted for the energy and show that it is indeed Joules if you put in the numbers? If yes, then the energy difference should also be in Joules.

 

[tomwilliam]

Don't forget that 1 J is equivalent to 1 kg m^2 s^-2

So if you have final units of J^2 kg^-1 m^-2 s^2...try converting the J^2 into its component SI units and see what you get!

 

[Kawakaze]

Wow thanks for the two speedy responses. Kuruman, I don't understand you, this is a little beyond me at the minute (the unit is an introduction to quantum physics! =) ) I do not know what the units are, its all SI and Plancks constant is in J s, so I assume it is joules.

Tom, I tried that and got a crazy answer. I just tried it again and got the final unit to be the joule. I squared the kg but not the rest of the units! Thanks I think I can take it from here. =)

 

[Kawakaze]

Could someone kindly confirm my answers?

I got the energy of the released photon to be 13.72 x 10^-20 J

The wavelength of the photon is got to be 1448 nm. I got again weird units. J kg^-1 m^-1, I would expect units of metres, the best i can cancel to is m s^-2, the unit of acceleration? and also is not this answer out of the visible spectrum. Nothing said about it in the question, but most of our questions in the book deal with light photons and not the rest of the EM range, makes me wonder...

Perhaps it is because this paper is due tomorrow, I am making stupid mistakes. Perhaps a full time job is not giving me much left out of the 21 days I had to study this 300 page book.