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
·
