22.
(a) From Eq. 38-47,
Q
=
−∆m c
2
= (m
Λ
0
− m
p
− m
π
−
)c
2
=
1115.6 MeV
− 938.3 MeV − 139.6 MeV = 37.7 MeV .
(b) We use the formula obtained in problem 11 (where it should be emphasized that E is used to mean
the rest energy, not the total energy):
K
p
=
1
2E
Λ
(E
Λ
− E
p
)
2
− E
2
π
=
(1115.6 MeV
− 938.3 MeV)
2
− (139.6 MeV)
2
2(1115.6 MeV)
= 5.35 MeV .
(c) By conservation of energy,
K
π
−
= Q
− K
p
= 37.7 MeV
− 5.35 MeV = 32.4 MeV .