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15. (a) The de Broglie wavelength is given by
λ
=
h/p
,where
p
is the magnitude of the momentum. The
kinetic energy
K
and momentum are related by Eq. 3851, which yields
pc
=
p
K
2
+2
Kmc
2
=
p
(200 MeV)
2
+ 2(200 MeV)(0
.
511 MeV) = 200
.
5MeV
.
Thus,
λ
=
hc
pc
=
1240 eV
·
nm
200
.
5
×
10
6
eV
=6
.
18
×
10
−
6
nm = 6
.
18 fm
.
(b) The diameter of a copper nucleus, for example, is about 8
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 Fall '08
 SPRUNGER
 Physics, Energy, Kinetic Energy, Momentum

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