# Photon emitted when proton changes state

1. Mar 4, 2013

### wahaj

1. The problem statement, all variables and given/known data
a proton is confined in an infinitely high square well of length 10 fm. If the proton transitions from n=2 to ground state determine the energy and wavelength of the photon emitted

2. Relevant equations

$$E = \frac{h^2 n^2}{8mL^2}$$
$$E = \frac{hc}{\lambda} \ \ or \ \ \lambda = \frac{hc}{E}$$

3. The attempt at a solution
I need some one to tell me if I did this right.
energy at n = 2
$$E_1 = \frac{(6.626E-34)^2( 2^2) }{8(1.67E-27)(1E-14)^2}$$
$$E_1 = 1.31E-12$$

energy at ground state
$$E_0 = \frac { (6.626E-34)^2}{8(1.67E-27)(1E-14)^2 }$$
$$E_0 = 3.286E-13$$

energy of photon released
$$E = E_1 - E_0$$
$$E = 9.859E-13 \ J$$

wavelength of photon
$$\lambda = \frac{(6.626E-34)(3E8)}{9.859E-13}$$
$$\lambda = 2.016E-13 m = 0.2016 pm$$
this would be a gamma ray.

So did I do this question right?

2. Mar 5, 2013

### Staff: Mentor

There are some units missing, but a gamma ray is the right order of magnitude for such a photon and the approach looks fine. You can check the calculations with WolframAlpha, for example.

3. Mar 5, 2013

thanks.