62.
(a) Since K = 7.5 MeV
m
α
c
2
= 4(932 MeV), we may use the non-relativistic formula p =
√
2m
α
K.
Using Eq. 38-43 (and recognizing that 1240 eV
·nm = 1240 MeV·fm), we obtain
λ =
h
p
=
hc
√
2m
α
c
2
K
=
1240 MeV
·fm
2(4 u)(931.5 MeV/u)(7.5 MeV)
= 5.2 fm .
(b) Since λ = 5.2 fm
30 fm, to a fairly good approximation, the wave nature of the α particle does
not need to be taken into consideration.