The ratio of specific charge of an electron to that of a protons is

Options

A. `1:1`
B. ` 1837:1`
C. `1:1837`
D. `2:1`

Answer

To find the ratio of the specific charge of an electron to that of a proton, we can follow these steps:

### Step-by-Step Solution:

1. **Understand Specific Charge**:
The specific charge is defined as the charge of a particle divided by its mass. Mathematically, it is given by:
\[ \text{Specific Charge} = \frac{\text{Charge}}{\text{Mass}} \]

2. **Identify Charges and Masses**:
- The charge of an electron (e) is approximately \( -1.6 \times 10^{-19} \) coulombs (we will use the magnitude, which is \( 1.6 \times 10^{-19} \) C).
- The charge of a proton is also \( +1.6 \times 10^{-19} \) coulombs.
- The mass of an electron (\( m_e \)) is approximately \( 9.11 \times 10^{-31} \) kg.
- The mass of a proton (\( m_p \)) is approximately \( 1.67 \times 10^{-27} \) kg.

3. **Calculate Specific Charge for Electron**:
\[ \text{Specific Charge of Electron} = \frac{\text{Charge of Electron}}{\text{Mass of Electron}} = \frac{1.6 \times 10^{-19}}{9.11 \times 10^{-31}} \, \text{C/kg} \]

4. **Calculate Specific Charge for Proton**:
\[ \text{Specific Charge of Proton} = \frac{\text{Charge of Proton}}{\text{Mass of Proton}} = \frac{1.6 \times 10^{-19}}{1.67 \times 10^{-27}} \, \text{C/kg} \]

5. **Formulate the Ratio**:
The ratio of the specific charge of an electron to that of a proton is given by:
\[ \text{Ratio} = \frac{\text{Specific Charge of Electron}}{\text{Specific Charge of Proton}} = \frac{\frac{1.6 \times 10^{-19}}{9.11 \times 10^{-31}}}{\frac{1.6 \times 10^{-19}}{1.67 \times 10^{-27}}} \]

6. **Simplify the Ratio**:
The charge values cancel out:
\[ \text{Ratio} = \frac{1.67 \times 10^{-27}}{9.11 \times 10^{-31}} = \frac{1.67}{9.11} \times 10^{3} \approx 1837 \]

7. **Final Result**:
Thus, the ratio of the specific charge of an electron to that of a proton is:
\[ \text{Ratio} = 1837 : 1 \]

### Conclusion:
The correct answer is that the ratio of the specific charge of an electron to that of a proton is \( 1837 : 1 \).