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Test Index
Atoms and Nuclei
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Section:
Physics
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© examsnet.com
Question : 8 of 51
Marks:
+1
,
-0
A heavy nucleus
N
, at rest, undergoes fission
N
→
P
+
Q
, where
P
and
Q
are two lighter nuclei. Let
δ
=
M
N
−
M
P
−
M
Q
where
M
P
M
Q
and
M
N
are the masses of
P
,
Q
and
N
, respectively.
E
P
and
E
Q
are the kinetic energies of
P
and
Q
, respectively. The speeds of
P
and
Q
are
v
P
and
v
Q
respectively. If
c
is the speed of light, which of the following statement(s) is(are) correct ?
[JEE Adv 2021 P2]
E
P
+
E
Q
=
c
2
δ
E
P
=
(
M
P
∕
M
P
+
M
Q
)
c
2
δ
v
P
∕
v
Q
=
M
Q
∕
M
p
The magnitude of momentum for
P
as well as
Q
is
c
√
2
µ
δ
, where
µ
=
M
P
M
Q
∕
(
M
P
+
M
Q
)
Validate
Solution:
For nuclear fission reaction,
N
→
P
+
Q
Energy released
=
∆
M
c
2
=
(
M
N
−
M
P
−
M
Q
)
c
2
=
δ
=
c
2
This will be distributed as kinetic energy of
P
and
Q
∴
E
p
+
E
q
=
δ
c
2
.....(i)
By conservation of momentum
V
P
M
P
=
V
Q
M
Q
∴
V
P
V
q
=
M
q
M
p
.....(ii)
Kinetic energy be written as
K
E
=
P
2
2
m
Hence divided in inverse ratio of masses
E
P
=
M
q
M
P
+
M
q
c
2
δ
....(iii)
By equation (i)
⇒
P
2
2
M
P
+
P
2
2
M
q
=
δ
c
2
⇒
P
2
2
µ
=
δ
c
2
⇒
P
=
c
√
2
µ
δ
[
∵
µ
=
M
P
M
Q
M
P
+
M
Q
]
© examsnet.com
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