The mass of an electron is _______ times that of mass of a proton.

Explanation

To solve the question regarding the mass of an electron in relation to the mass of a proton, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Mass of an Electron and Proton**:
- The mass of an electron (m_e) is approximately \(9.67 \times 10^{-31}\) kg.
- The mass of a proton (m_p) is approximately \(1.67 \times 10^{-27}\) kg.

2. **Set Up the Ratio**:
- We need to find the ratio of the mass of an electron to the mass of a proton, which can be expressed as:
\[ \text{Ratio} = \frac{m_e}{m_p} \]

3. **Substitute the Values**:
- Substitute the known values into the ratio:
\[ \text{Ratio} = \frac{9.67 \times 10^{-31} \text{ kg}}{1.67 \times 10^{-27} \text{ kg}} \]

4. **Perform the Calculation**:
- Calculate the ratio:
\[ \text{Ratio} = \frac{9.67}{1.67} \times \frac{10^{-31}}{10^{-27}} = \frac{9.67}{1.67} \times 10^{-4} \]
- Now, calculate \( \frac{9.67}{1.67} \):
\[ \frac{9.67}{1.67} \approx 5.79 \]
- Therefore, the ratio becomes:
\[ \text{Ratio} \approx 5.79 \times 10^{-4} \]

5. **Express the Ratio in Terms of Proton Mass**:
- To express the mass of an electron in terms of the mass of a proton, we can write:
\[ m_e \approx \frac{1}{1838} m_p \]
- This means that the mass of an electron is approximately \( \frac{1}{1838} \) times that of the mass of a proton.

### Final Answer:
The mass of an electron is \( \frac{1}{1838} \) times that of the mass of a proton.

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