P307/P707 - Nuclei and Particle Physics
Assignment 2
Submission deadline : 14.02.25
1. (a) Predict the spin-parity using shell model for the ground states of B13
5, C13
6and N13
7.
(b) Order them according to mass with the lowest mass first. Justify your ordering.
(c) Roughly Estimate the energy difference between the two lowest mass members. 10
2. The mass difference between two mirror nuclei Si
27
14
and Al
27
13
is 6 MeV. Estimate their
radius. (neglecting proton-neutron mass difference). Compare with the theoretical formula
(r0= 1.3 fm). Also predict the spin-parity for the ground state using shell model. 10
3. (a) Predict the spin-parity using shell model for the ground states of Na
23
11
, Mn
55
25
and F
19
9
.
(b) The theoretical estimations do not agree with experimentally measured values. Comment
on the possible reasons. 10
4. Assume the potential of a simplified nucleus model as follows
V(x, y, z) = ∞for |x|,|y|,|z|>R
2
= 0 for |x|,|y|,|z|<R
2
Estimate the kinetic energy of the highest energy nucleon of Fe
56
28
.
R
is the nuclear diameter
which is roughly 10−12 cm. 10
5. Give physical reasoning for the following statements:
(a) The motion of individual nucleons inside a nucleus may be considered as independent
from each other. (b) All the even-even nuclei have 0+ground state. 10
6. U
238
originates from the solidification of the Earth’s crust occurred about 2.5 billions of
years ago. Assuming its half life as 4.5×109years, derive
{the fraction of U238 decayed so far
{the specific activity of U238 in Ci/g. 10
7. Consider the decay chain
X1→X2→X3
where the decay constants are
λ1
= 12
s−1
and
λ2
= 60
s−1
, respectively.
X3
is stable. Assume
that at
t
= 0, only
X1
was present with number
N0
. Compute the numbers of elements
(N1, N2, N3) present at time t. Find the ratio N3
N1after t=1
4second. 10