The charge to mass ratio of α
- particle is approximately is_____ of the charge to mass ratio of a proton is:
A. Half
B. Twice
C. Four times
D. Six times

To solve the question regarding the charge-to-mass ratio of an α-particle (alpha particle) in comparison to that of a proton, we need to understand the properties of both particles.

### Definitions

1. **Charge-to-mass ratio (q/m)**: This is defined as the amount of charge (q) divided by the mass (m) of the particle. It tells us how much charge a particle carries per unit of mass.

2. **Proton**:
- **Charge**: +1e (where e = elementary charge ≈ \(1.6 \times 10^{-19}\) C)
- **Mass**: Approximately \(1.67 \times 10^{-27}\) kg

3. **Alpha particle (α-particle)**:
- An α-particle consists of 2 protons and 2 neutrons (i.e., it is a helium nucleus).
- **Charge**: +2e (since it has 2 protons)
- **Mass**: Approximately \(4 \times 1.67 \times 10^{-27}\) kg (mass of 2 protons + 2 neutrons)

### Calculating Charge-to-Mass Ratios

1. **Charge-to-mass ratio of a proton**:
\[
\frac{q}{m}_{\text{proton}} = \frac{+1e}{m_{\text{proton}}} = \frac{+1 \times 1.6 \times 10^{-19}}{1.67 \times 10^{-27}} \, \text{C/kg}
\]

2. **Charge-to-mass ratio of an α-particle**:
\[
\frac{q}{m}_{\alpha} = \frac{+2e}{m_{\alpha}} = \frac{+2 \times 1.6 \times 10^{-19}}{4 \times 1.67 \times 10^{-27}} \, \text{C/kg}
\]

### Simplifying the Ratios

Now let's simplify the ratio of the α-particle to the proton:

1. **Charge-to-mass ratio of α-particle**:
\[
\frac{q}{m}_{\alpha} = \frac{2 \times 1.6 \times 10^{-19}}{4 \times 1.67 \times 10^{-27}} = \frac{2}{4} \times \frac{1.6 \times 10^{-19}}{1.67 \times 10^{-27}} = \frac{1}{2} \times \frac{1.6 \times 10^{-19}}{1.67 \times 10^{-27}}
\]

2. **Ratio of charge-to-mass ratio of α-particle to proton**:
\[
\text{Ratio} = \frac{\frac{q}{m}_{\alpha}}{\frac{q}{m}_{\text{proton}}} = \frac{\frac{1}{2} \times \frac{1.6 \times 10^{-19}}{1.67 \times 10^{-27}}}{\frac{1.6 \times 10^{-19}}{1.67 \times 10^{-27}}} = \frac{1}{2}
\]

### Conclusion

The charge-to-mass ratio of the α-particle is half that of the proton. Therefore, the answer to the question is:

**A. Half**