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JEE Mains 29-July-2022 Shift 2 Solved Paper
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© examsnet.com
Question : 41
Total: 90
Read the following statements:
(A) Volume of the nucleus is directly proportional to the mass number.
(B) Volume of the nucleus is independent of mass number.
(C) Density of the nucleus is directly proportional to the mass number.
(D) Density of the nucleus is directly proportional to the cube root of the mass number.
(E) Density of the nucleus is independent of the mass number.
Choose the correct option from the following options.
[29-Jul-2022-Shift-2]
(A) and (D) only.
(A) and (E) only.
(B) and (E) only.
(A) and (C) only.
Validate
Solution:
We know,
Radius of nucleus,
r
=
r
0
A
1
3
where,
A
=
mass number
∴
Volume
(
v
)
=
4
3
π
r
3
=
4
3
π
r
0
3
⋅
A
∴
v
∝
A
∴
Volume is directly proportional to mass number.
We know,
density
(
d
)
=
m
v
=
z
m
p
+
(
A
−
z
)
m
N
4
3
π
r
0
3
(
A
1
∕
3
)
3
=
z
m
p
+
A
m
p
−
z
m
p
4
3
π
r
0
3
A
[
∵
m
p
≃
m
N
]
=
A
m
p
4
3
π
r
0
3
A
=
m
p
4
3
π
r
0
3
∴
Density of nucleus is independent of mass number.
© examsnet.com
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