Nuclei Practice Questions - DPP for JEE

 Page 1


PART-I (Single Correct MCQs)
]1. Binding energy per nucleon versus mass number
curve for nuclei is shown in the figure. W, X, Y and
Z are four nuclei indicated on the curve. The process
that would release energy is
(a)
(b)
(c)
(d)
2. The decay constants of a radioactive substance for a and ß emission are
?
a
 and ?
ß
 respectively. If the substance emits a and ß simultaneously,
then the average half life of the material will be
(a)
(b)
Page 2


PART-I (Single Correct MCQs)
]1. Binding energy per nucleon versus mass number
curve for nuclei is shown in the figure. W, X, Y and
Z are four nuclei indicated on the curve. The process
that would release energy is
(a)
(b)
(c)
(d)
2. The decay constants of a radioactive substance for a and ß emission are
?
a
 and ?
ß
 respectively. If the substance emits a and ß simultaneously,
then the average half life of the material will be
(a)
(b)
(c)
(d)
3. Radioactive element decays to form a stable nuclide. The rate of decay
of reactant is correctly depicted by
(a) (b) (c)
(d)
4. A nucleus of mass M + ?m is at rest and decays into two daughter
nuclei of equal mass  each. Speed of light is c.
The speed of daughter nuclei is
(a)
(b)
(c)
(d)
5. The radioactivity of a sample is R
1
 at a time T
1
 and R
2
 at a time T
2
. If
the half-life of the specimen is T, the number of atoms that have
disintegrated in the time (T
1
 – T
2
) is proportional to
(a) (R
1
T
1
 – R
2
T
2
)
Page 3


PART-I (Single Correct MCQs)
]1. Binding energy per nucleon versus mass number
curve for nuclei is shown in the figure. W, X, Y and
Z are four nuclei indicated on the curve. The process
that would release energy is
(a)
(b)
(c)
(d)
2. The decay constants of a radioactive substance for a and ß emission are
?
a
 and ?
ß
 respectively. If the substance emits a and ß simultaneously,
then the average half life of the material will be
(a)
(b)
(c)
(d)
3. Radioactive element decays to form a stable nuclide. The rate of decay
of reactant is correctly depicted by
(a) (b) (c)
(d)
4. A nucleus of mass M + ?m is at rest and decays into two daughter
nuclei of equal mass  each. Speed of light is c.
The speed of daughter nuclei is
(a)
(b)
(c)
(d)
5. The radioactivity of a sample is R
1
 at a time T
1
 and R
2
 at a time T
2
. If
the half-life of the specimen is T, the number of atoms that have
disintegrated in the time (T
1
 – T
2
) is proportional to
(a) (R
1
T
1
 – R
2
T
2
)
(b) (R
1
 – R
2
)
(c) (R
1
 – R
2
)/T
(d) (R
1
 – R
2
) T 
6. A nucleus disintegrates into two nuclear parts which have their
velocities in the ratio 2 : 1. Ratio of their nuclear sizes will be
(a) 2
1/3
 : 1
(b) 1 : 3
1/2
(c) 3
1/2 
: 1
(d) 1 : 2
1/3
7. The energy spectrum of ß-particles [Number N(E) as a function of ß-
energy E] emitted from a radioactive source is
(a)
(b)
(c)
(d)
8. If M (A; Z), M
p
 and M
n
 denote the masses of the nucleus  proton
and neutron respectively  in units of u ( 1u = 931.5 MeV/c
2
) and  BE
represents its bonding energy in MeV, then
Page 4


PART-I (Single Correct MCQs)
]1. Binding energy per nucleon versus mass number
curve for nuclei is shown in the figure. W, X, Y and
Z are four nuclei indicated on the curve. The process
that would release energy is
(a)
(b)
(c)
(d)
2. The decay constants of a radioactive substance for a and ß emission are
?
a
 and ?
ß
 respectively. If the substance emits a and ß simultaneously,
then the average half life of the material will be
(a)
(b)
(c)
(d)
3. Radioactive element decays to form a stable nuclide. The rate of decay
of reactant is correctly depicted by
(a) (b) (c)
(d)
4. A nucleus of mass M + ?m is at rest and decays into two daughter
nuclei of equal mass  each. Speed of light is c.
The speed of daughter nuclei is
(a)
(b)
(c)
(d)
5. The radioactivity of a sample is R
1
 at a time T
1
 and R
2
 at a time T
2
. If
the half-life of the specimen is T, the number of atoms that have
disintegrated in the time (T
1
 – T
2
) is proportional to
(a) (R
1
T
1
 – R
2
T
2
)
(b) (R
1
 – R
2
)
(c) (R
1
 – R
2
)/T
(d) (R
1
 – R
2
) T 
6. A nucleus disintegrates into two nuclear parts which have their
velocities in the ratio 2 : 1. Ratio of their nuclear sizes will be
(a) 2
1/3
 : 1
(b) 1 : 3
1/2
(c) 3
1/2 
: 1
(d) 1 : 2
1/3
7. The energy spectrum of ß-particles [Number N(E) as a function of ß-
energy E] emitted from a radioactive source is
(a)
(b)
(c)
(d)
8. If M (A; Z), M
p
 and M
n
 denote the masses of the nucleus  proton
and neutron respectively  in units of u ( 1u = 931.5 MeV/c
2
) and  BE
represents its bonding energy in MeV, then
(a) M (A, Z) = ZM
p
 + (A – Z) M
n
 –BE/c
2
(b) M (A, Z) = ZM
p
+ ( A–Z) M
n
 + BE
(c) M (A, Z) = ZM
p
 + (A – Z) M
n
 – BE
(d) M (A, Z) = ZM
p
 + (A – Z)M
n
 + BE/c
2
9. If radius of the  nucleus is taken to be R
Al
, then the radius of 
nucleus is nearly:
(a)
(b)
(c)
(d)
10. Binding energy per nucleon plot against the mass
number for stable nuclei is shown in the figure.
Which curve is correct?
(a) A
(b) B
(c) C
(d) D
11. At time t = 0, N
1
 nuclei of decay constant  and N
2
 nuclei of decay
constant ?
2
 are mixed. The decay rate of mixture is
(a)
(b)
(c)
Page 5


PART-I (Single Correct MCQs)
]1. Binding energy per nucleon versus mass number
curve for nuclei is shown in the figure. W, X, Y and
Z are four nuclei indicated on the curve. The process
that would release energy is
(a)
(b)
(c)
(d)
2. The decay constants of a radioactive substance for a and ß emission are
?
a
 and ?
ß
 respectively. If the substance emits a and ß simultaneously,
then the average half life of the material will be
(a)
(b)
(c)
(d)
3. Radioactive element decays to form a stable nuclide. The rate of decay
of reactant is correctly depicted by
(a) (b) (c)
(d)
4. A nucleus of mass M + ?m is at rest and decays into two daughter
nuclei of equal mass  each. Speed of light is c.
The speed of daughter nuclei is
(a)
(b)
(c)
(d)
5. The radioactivity of a sample is R
1
 at a time T
1
 and R
2
 at a time T
2
. If
the half-life of the specimen is T, the number of atoms that have
disintegrated in the time (T
1
 – T
2
) is proportional to
(a) (R
1
T
1
 – R
2
T
2
)
(b) (R
1
 – R
2
)
(c) (R
1
 – R
2
)/T
(d) (R
1
 – R
2
) T 
6. A nucleus disintegrates into two nuclear parts which have their
velocities in the ratio 2 : 1. Ratio of their nuclear sizes will be
(a) 2
1/3
 : 1
(b) 1 : 3
1/2
(c) 3
1/2 
: 1
(d) 1 : 2
1/3
7. The energy spectrum of ß-particles [Number N(E) as a function of ß-
energy E] emitted from a radioactive source is
(a)
(b)
(c)
(d)
8. If M (A; Z), M
p
 and M
n
 denote the masses of the nucleus  proton
and neutron respectively  in units of u ( 1u = 931.5 MeV/c
2
) and  BE
represents its bonding energy in MeV, then
(a) M (A, Z) = ZM
p
 + (A – Z) M
n
 –BE/c
2
(b) M (A, Z) = ZM
p
+ ( A–Z) M
n
 + BE
(c) M (A, Z) = ZM
p
 + (A – Z) M
n
 – BE
(d) M (A, Z) = ZM
p
 + (A – Z)M
n
 + BE/c
2
9. If radius of the  nucleus is taken to be R
Al
, then the radius of 
nucleus is nearly:
(a)
(b)
(c)
(d)
10. Binding energy per nucleon plot against the mass
number for stable nuclei is shown in the figure.
Which curve is correct?
(a) A
(b) B
(c) C
(d) D
11. At time t = 0, N
1
 nuclei of decay constant  and N
2
 nuclei of decay
constant ?
2
 are mixed. The decay rate of mixture is
(a)
(b)
(c)
(d) 
12. A radioactive nucleus of mass number A, initially at rest, emits an a-
particle with a speed v. The recoil speed of daughter nucleus is
(a)
(b)
(c)
(d)
13. Consider a radioactive material of half-life 1.0 minute. If one of the
nuclei decays now, the next one will decay
(a) after 1 minute
(b) after 
(c) after  minute, where N is the number of nuclei present at that moment
(d) after any time
14. The ratio of half-life times of two elements A and B is . The ratio
of respective decay constant  is
(a) T
B
 / T
A
(b) T
A
 / T
B
(c)
(d)
15. In a radioactive material the activity at time t
1
 is R
1
 and at a later time t
2
,