Fundamental particles — practice questions

1. Identify the composition of the nucleus: A helium nucleus (⁴₂He) contains 2 protons and 2 neutrons (since Nucleon number A = 4 and Proton number Z = 2, Neutron number N = A - Z = 4 - 2 = 2).
2. Calculate the total charge (Q): The charge is due to the 2 protons. Neutrons are neutral. Q = 2 × (charge of a proton) = 2 × e Q = 2 × (1.60 × 10⁻¹⁹ C) = 3.20 × 10⁻¹⁹ C
3. Calculate the total mass (M): The mass is the sum of the masses of the 2 protons and 2 neutrons. M = (2 × mₚ) + (2 × mₙ) M = (2 × 1.673 × 10⁻²⁷ kg) + (2 × 1.675 × 10⁻²⁷ kg) M = (3.346 × 10⁻²⁷ kg) + (3.350 × 10⁻²⁷ kg) M = 6.696 × 10⁻²⁷ kg
4. Calculate the specific charge: Use the formula: Specific charge = Charge / Mass. Specific charge = (3.20 × 10⁻¹⁹ C) / (6.696 × 10⁻²⁷ kg) Specific charge ≈ 4.78 × 10⁷ C/kg

Answer: The specific charge of a helium nucleus is approximately 4.78 × 10⁷ C kg⁻¹.

1. Recall that alpha decay involves the emission of an alpha particle (⁴₂α), which is a helium nucleus with 2 protons and 2 neutrons.
2. The nucleon number (A) of the parent nucleus decreases by 4. So, new A = 232 - 4 = 228.
3. The proton number (Z) of the parent nucleus decreases by 2. So, new Z = 90 - 2 = 88.
4. The daughter nucleus therefore has a nucleon number of 228 and a proton number of 88 (Radium-228, ²²⁸₈₈Ra).