Tutorial 14 — Atomic Physics

Course: FAD1022 Basic Physics 2
Semester: 2 2025/2026
Centre: Centre for Foundation Studies in Science, Universiti Malaya (PASUM)

Given Constants

Constant Value
$r_0$ $1.2 \times 10^{-15} \text{ m}$
Mass of Proton $1.007276 \text{ u}$
Mass of Neutron $1.008665 \text{ u}$
1 u $931.5 \text{ MeV/c}^2$
Avogadro Number $6.022 \times 10^{23} \text{ mol}^{-1}$

Question 1

Using a standard periodic table and your knowledge of nuclear physics, determine the physical properties of a Gold-197 nucleus ($^{197}_{79}\text{Au}$).

Determine:

  • Mass Number, A:
  • Proton Number, Z:
  • Neutron, N:
  • Radius, R:
  • Volume, V:

Question 2

Uranium is a heavy radioactive element commonly used as fuel in nuclear reactors and in nuclear weapons. It occurs naturally in several isotopes, the most prominent being Uranium-238 ($^{238}{92}\text{U}$) and Uranium-235 ($^{235}{92}\text{U}$).

Prove Uranium-235 is more stable compared to its isotope Uranium-238.

Given:

  • Mass of Uranium-235 nucleus: $235.043929 \text{ u}$
  • Mass of Uranium-238 nucleus: $238.050788 \text{ u}$

Question 3

The table below provides the atomic masses of selected nuclides:

Nuclide Atomic Mass (u)
$^4_2\text{He}$ 4.00260
$^{23}_{11}\text{Na}$ 22.98987
$^{27}_{13}\text{Al}$ 26.98154

Using the data provided, evaluate whether it is possible for $^{27}_{13}\text{Al}$ to undergo spontaneous alpha decay.

Hint: spontaneous alpha decay means that the mass defect should be positive

Question 4

A sample of a radioactive isotope, Technetium-99m (Tc-99m) is commonly used in medical imaging. A hospital receives a 2.0 µg sample of pure Tc-99m.

Given information:

  • Half-life of Tc-99m: 6.0 hours
  • Mass of Tc-99m: $98.9063 \text{ u}$

Calculate:

a) The initial number of Tc-99m atoms ($N_0$) in the 2.0 µg sample b) The decay constant c) The activity after 12 hours (unit must be Bq) d) How long will it take for the activity of this Tc-99m sample to decay to 10% of its initial activity

Question 5

A uranium-235 ($^{235}{92}\text{U}$) nucleus absorbs a neutron and undergoes nuclear fission. In the process, it splits into a bromine-85 nucleus ($^{85}{35}\text{Br}$), a lanthanum-148 ($^{148}_{x}\text{La}$) nucleus, and free neutrons.

Atomic masses:

  • Uranium-235: $235.04393 \text{ u}$
  • Neutron: $1.008665 \text{ u}$
  • Bromine-85: $84.91274 \text{ u}$
  • Lanthanum-148: $147.921230 \text{ u}$

Based on the information given:

a) Write the nuclear reaction and determine the number of protons for La b) Calculate energy released from the reaction

Related Concepts

  • Atomic Physics
  • Nuclear Physics
  • Atomic Nucleus
  • Nuclear Structure
  • Mass Number
  • Atomic Number
  • Nuclear Radius ($R = r_0 A^{1/3}$)
  • Binding Energy
  • Mass Defect
  • Alpha Decay
  • Nuclear Fission
  • Radioactivity
  • Half-Life
  • Decay Constant ($\lambda = \frac{\ln 2}{t_{1/2}}$)
  • Activity ($A = \lambda N$)
  • Exponential Decay
  • Technetium-99m

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