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QUESTION: 1

The mass number of an element in a radioactive series is 223. The radioactive series is

Solution:

Mass number of radioactive element = 223

This mass number can be written in the form of 4n + 2, which coresponds to Uranium series.

QUESTION: 2

A nucleus having mass number A decays by α - emission to the ground state of its daughter nucleus. The Q value of the process is E. The energy of the a - panicle is

Solution:

For α -particle emission, the kinetic energy of α -particle is given by

Kinetic Energy = Q x where Q is energy released during α - decay process.

QUESTION: 3

Assuming that a nucleus is a sphere of nuclear matter of radius 1.2 x A^{1/3} fm, the average nucleon density in S.l. units is; approximately

Solution:

The radius of nuclear matter is given by

The nucleon density

*Answer can only contain numeric values

QUESTION: 4

The ratio of radii of U^{238} and He^{4} nuclei is_______________(upto one decimal place)

Solution:

*Answer can only contain numeric values

QUESTION: 5

Mass of α - particle = 4.002603 amu, mass of proton = 1.007825 amu, mass of neutron = 1.008664 amu. Taking 1 amu = 931 MeV, the binding energy of a-panicle is________(upto two decimal places).

Solution:

Binding energy o f a -particle

QUESTION: 6

The empirical mass formula (neglecting a term representing the odd-even effect) is

where α, β, γ and ε are constants. The expression for the value of Z which corresponds to the most stable nucleus for a set of isobars of mass number A is

Solution:

QUESTION: 7

The radius of G e is measured to be twice the radius of _{4}Be^{9}. The number of nucleons in Ge is

Solution:

The radius of Ge = 2 x radius of _{4}Be^{9}.

QUESTION: 8

Which one of the following statement regarding neutrino is wrong?

Solution:

Neutrino has spin-1/2,. zero charge (neutral), zero rest mass and does not interact with matter.

*Answer can only contain numeric values

QUESTION: 9

The half life of radon ls 3.8 days. After 15.2 days, N_{0 }/N will be________

Solution:

For Radon, T_{1/2} = 3.8 days

Now, number of half lives in 15.2 days = 15.2/ 3.8 = 4

*Answer can only contain numeric values

QUESTION: 10

The Q-value of the ^{3}H(p,n)^{3} He reaction is -0.764 MeV. The threshold energy (for appearance of neutrons in the forward direction is___________MeV. (upto two decimal places)

Solution:

The threshold energy for apperance of neutron in the forward direction is

QUESTION: 11

The distance of closest approach of α -particles to the Copper nucleus (Z = 29). when a-particles of 5 MeV energy are scattered back by a thin sheet of Copper, is

Solution:

Let the distance of closest approach of α - particle to copper nucleus is b.

QUESTION: 12

Al are mirror nuclei. Tlie former is a position emitter with E_{max} = 3.48 MeV. The value of radius constant (r_{0}) can be estimated as

Solution:

For positron emission,

QUESTION: 13

The expected value of shell-model quadmpole moment of^{209}Bi. if the ground state spin-parity of^{209}Bi is 9^{-}/2

Solution:

The spin of 209 Bi 9/2

*Answer can only contain numeric values

QUESTION: 14

If the binding energies of the mirror nuclei _{21}Sc^{41} and _{20}Ca^{41} are 343.143 MeV and 350.420 MeV, respectively. The radii of these nuclei by using the semi-empirical mass formula is__________fm (upto two decimal places)

Solution:

Difference in binding energies of _{21}Sc^{41} and _{20}Ca^{41} = 350.420 - 343.143 = 7.277 MeV

Since, Difference in binding energies of min or nuclei _{21}Se^{41} and _{20}Ca^{41} is equal to difference in Coulomb energies.

QUESTION: 15

Using semi-empirical mass formula, the most stable isobar with mass number A = 65. corresponds to

Solution:

F or A = 65, the most stable isobar corresponds to

QUESTION: 16

From the shell model prediction, the ground state spin and parity of nuclei, respectively.

Solution:

For

The shell structure of neutrons:

Therefore, last neutrons lies in shell.

Therefore, the nuclear spin of

The parity of

Hence, nuclear spin-parity of

Similarly for

The last proton lies in shell.

Hence, the nuclear spin-parity of

QUESTION: 17

The following interactions proceed through the strong, electromagnetic (EM) or weak interactions.

(i)

(ii)

(iii)

The correct order of interactions is

Solution:

is allowed via EM interaction because photon is involved.

is allowed via weak interaction because neutrino (Lepton) is involved.

is allowed via strong interaction because Barvons are involved.

QUESTION: 18

Which one of the following reaction is NOT forbidden ?

Solution:

(a) forbidden because energy is not conserved.

(b) forbidden because Baryon number is violated.

(c) allowed by strong interaction because ΔS = 0 and other quantum numbers are conserved.

(d) forbidden because Lepton number is not conserved.

QUESTION: 19

Consider the decay of K° meson of momentum P_{0} into ,π^{+} and π^{-} of momenta p_{+} and p_ m the opposite direction such that p_{+} = 2p_. The value of p_{0} is given by

Solution:

∴

i.e.

Squaring both sides,

⇒

⇒

Squaring again,

⇒

⇒

⇒

*Answer can only contain numeric values

QUESTION: 20

The ground state magnetic moment of ^{33}S_{16} is_____________μN.

Solution:

The nucleus has 16 protons and 17 neutrons.

The shell structure of neutrons:

Since, last neutron lies in shell.

Therefore, the nuclear spin

The magnetic moment of last neutron in state is given by

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