The nuclear potential that binds protons and neutrons in the nucleus of an atom is often approximated by a square well. imagine a proton conned in an innite square well of length 105 nm, a typical nuclear diameter. calculate the wavelength and energy associated with the photon that is emitted when the proton undergoes a transition from the rst excited state (n 2) to the ground state (n 1). in what region of the electromagnetic spectrum does this wavelength belong?

3. The nuclear potential that binds protons and neutrons in the nucleus of an atom

is often approximated by a square well. Imagine a proton confined in an infinite

square well of length 10−5 nm, a typical nuclear diameter. Calculate the wavelength

and energy associated with the photon that is emitted when the proton undergoes a

transition from the first excited state (n = 2) to the ground state (n = 1). In what

region of the electromagnetic spectrum does this wavelength belong?

Answer 3

We are given that,

Length of square well = L = 10−5

nm = 10−14 m.

Energy of proton in state n is given by,

En =

π

2n

2~

2

2mpL2

,

where L is the width of the square well.

⇒ E1 =

π

2~

2

2mpL2

E2 =

4π

2~

2

2mpL2

·

3.2x10^7