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 will follow these steps:

### Step-by-Step Solution:

1. **Define Specific Charge**:
The specific charge is defined as the ratio of charge to mass. For any particle, it can be expressed as:
\[ \text{Specific Charge} = \frac{\text{Charge}}{\text{Mass}} \]

2. **Write the Formula for Electron and Proton**:
For an electron, the specific charge (\(S_e\)) is:
\[ S_e = \frac{e}{m_e} \]
For a proton, the specific charge (\(S_p\)) is:
\[ S_p = \frac{e}{m_p} \]
where \(e\) is the magnitude of the charge (same for both particles), \(m_e\) is the mass of the electron, and \(m_p\) is the mass of the proton.

3. **Calculate the Ratio of Specific Charges**:
The ratio of the specific charge of an electron to that of a proton is given by:
\[ \frac{S_e}{S_p} = \frac{\frac{e}{m_e}}{\frac{e}{m_p}} = \frac{m_p}{m_e} \]

4. **Substitute the Mass Relationship**:
We know that the mass of a proton is approximately 1837 times the mass of an electron:
\[ m_p = 1837 \times m_e \]
Therefore, substituting this into the ratio gives:
\[ \frac{S_e}{S_p} = \frac{1837 \times m_e}{m_e} = 1837 \]

5. **Final Result**:
Thus, the ratio of the specific charge of an electron to that of a proton is:
\[ \frac{S_e}{S_p} = 1837 \]

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

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