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.