SP025 Module Mutual - Perak Matriculation College

Nageswary & Mimi Erlieza
Nuclear and Particle Physics

Example 99:

The binding energy of deuterium 2 H is 2.25 MeV. Calculate the binding energy per nucleon of deuterium.
1

Solution:

EB = 2.25 = 1.125 MeV/ nucleon
A2

Exercise 99-1: Exercise 99-2:

Calculate the binding energy per nucleon of helium The binding energy per nucleon of Uranium-235 is
7.6 MeV/ nucleon. Calculate the binding energy of a
4 He if its binding energy is 28.3 MeV. uranium nucleus.
2
[1786 MeV]
[7.08 MeV/nucleon]

99

Ummi Atiah & Mimi Erlieza
Nuclear and Particle Physics

CHAPTER 11: NUCLEAR & PARTICLE PHYSICS
11.2 Radioactivity

L/O 11.2 b) State and use decay law dN
= decay rate/ activity
dN = −N
dt
dt
 = decay constant
N = number of remaining nuclei

Example 100:

A sample of radioisotope thorium-234 with a decay constant of 3.27 10−7 s−1 has a decay rate of
6.11014 decays per second. Calculate the number of remaining nuclei.

Solution:

dN = −N (ignore negative)
dt
6.11014 = −(3.27 10−7 )N

N = 1.87 1021nuclei

Exercise 100-1: Exercise 100-2:
A sample of radioisotope thorium-228 with a decay A radium-228 isotope decays with a decay rate of

constant of 7.2110−7 s−1 has a decay rate of 4.551014 particles per second by emitting

2 1014 decays per second. Calculate the alpha particle into radium-224 nucleus. After the
decay, the number of remaining nuclei is
number of remaining nuclei. N = 3.96 10 22 nuclei . Calculate the decay
constant.
[ 2.81020 nuclei ]
[1.15 10−8 s−1 ]

.

100

L/O 11.2 (d) :Use Siti Farahiyah & Mimi Erlieza
Nuclear and Particle Physics
N = No e−t
where
λ = decay constant
N = initial number of radioactive nuclei in the sample

0

N = number of nuclei remaining after time t

Example 101:
The decay constant of a given nucleus is 0.6 day -1. If the initial number of nuclide A is 8.01010, calculate
the remaining nuclei after 10 days.

Solution:

N = No e−t

( )= 8.0 1010 e−(0.6)(10)

= 1.98 108 nuclei

Exercise 101-1: Exercise 101-2:
The decay constant of a given nucleus is 5.4 x 10-3 s-1.
80% of a radioactive substance decays in 4.0 days.
If the initial number of nuclide A is 1.01020, calculate
Determine the decay constant,
the remaining nuclei after 5 minutes. [ . − ]
[ . × ]

101

L/O 11.2 (d) :Use Siti Farahiyah & Mimi Erlieza
Nuclear and Particle Physics
A = Ao e−t
where,
λ = decay constant
A= activity at time t
A = activity at time, t =0

0

Example 102:
A radioisotope has an initial activity 9 mCi. If the decay constant is 2 hours-1 , calculate activity of nuclei

after 16 hours.

Solution:

A = Ao e−t

( )= 9 10 −3 e−(2 )(16)

= 5.53 10−8 Ci

Exercise 102-1: Exercise 102-2:
The decay constant of a radioisotope is 6.66 x 10-7 s-1. The initial 131I prepared is 14925 Ci. Three
If its initial activity is 8 x 1010 Bq, calculate the
days after it was prepared, its activity was
activity of nuclei after 5 days
[5.99 x 1010 Bq] 0.50 µCi. Calculate the decay constant.
[8.04 day-1]

102

Mohd Khairul Azmi & Mimi Erlieza
Nuclear and Particle Physics

L/O 11.2 e) Define and use half-life,

T1 = ln 2 T1 = half-life

2  2

 = decay constant

Example 103:
A sample of radioisotope with a decay constant of 1.86 10−4 s−1 . Calculate the half-life of the
radioisotope.

Solution:

T1 = ln 2 = ln 2 −4 = 3.73 x103s = 1.04 hours
 1.86 x10
2

Exercise 103-1: Exercise 103-2:
Calculate the half-life of a sample of radioisotope with The half-life of a radioisotope is 3.8 days. Calculate
decay constant of 7.2110−7 s−1 . the decay constant.

[11.13days ] [ 2.1110−6 s−1 ]

103