To determine which subatomic particle has the greatest ratio of charge to mass, we need to analyze the charge and mass of each particle mentioned in the options: proton, alpha particle, neutron, and electron.
### Step 1: Identify the charge and mass of each particle
- **Proton (p)**: Charge = +1e (approximately +1.6 x 10^-19 C), Mass = 1.67 x 10^-27 kg
- **Alpha particle (α)**: Charge = +2e (approximately +3.2 x 10^-19 C), Mass = 4.00 x 10^-27 kg (since it consists of 2 protons and 2 neutrons)
- **Neutron (n)**: Charge = 0, Mass = 1.67 x 10^-27 kg
- **Electron (e)**: Charge = -1e (approximately -1.6 x 10^-19 C), Mass = 9.11 x 10^-31 kg
### Step 2: Calculate the charge to mass ratio for each particle
The charge to mass ratio (q/m) can be calculated using the formula:
\[
\text{Charge to mass ratio} = \frac{\text{Charge}}{\text{Mass}}
\]
1. **Proton**:
\[
\frac{q}{m} = \frac{+1.6 \times 10^{-19} \, \text{C}}{1.67 \times 10^{-27} \, \text{kg}} \approx 9.58 \times 10^{7} \, \text{C/kg}
\]
2. **Alpha particle**:
\[
\frac{q}{m} = \frac{+3.2 \times 10^{-19} \, \text{C}}{4.00 \times 10^{-27} \, \text{kg}} \approx 8.00 \times 10^{7} \, \text{C/kg}
\]
3. **Neutron**:
\[
\frac{q}{m} = \frac{0}{1.67 \times 10^{-27} \, \text{kg}} = 0 \, \text{C/kg}
\]
4. **Electron**:
\[
\frac{q}{m} = \frac{-1.6 \times 10^{-19} \, \text{C}}{9.11 \times 10^{-31} \, \text{kg}} \approx -1.76 \times 10^{11} \, \text{C/kg}
\]
### Step 3: Compare the ratios
Now we compare the charge to mass ratios calculated above:
- Proton: \(9.58 \times 10^{7} \, \text{C/kg}\)
- Alpha particle: \(8.00 \times 10^{7} \, \text{C/kg}\)
- Neutron: \(0 \, \text{C/kg}\)
- Electron: \(-1.76 \times 10^{11} \, \text{C/kg}\) (the absolute value is considered for comparison)
### Step 4: Determine the greatest ratio
The greatest ratio of charge to mass is for the electron, as its absolute value is significantly higher than that of the proton and alpha particle, and the neutron has no charge.
### Conclusion
The answer is **(D) Electron**.
