Question

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?

Answer 1

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

·