Which is true about an electron-

Options

A. rest mass of electron is `9.1xx10^(-28)g`
B. mass of electron increases with the increase in velocity
C. molar mass of electron is `5.48xx10^(-4)g//"mole"`
D. `e//m` of electron is `1.7xx10^(8) "coulomb"//g`

Answer

To determine which statements about an electron are true, we will analyze each statement step by step.

### Step 1: Analyze the first statement
**Statement:** The rest mass of an electron is \(9.1 \times 10^{-28}\) grams.

**Solution:**
- The known mass of an electron is \(9.1 \times 10^{-31}\) kilograms.
- To convert this to grams, we use the conversion factor \(1 \text{ kg} = 1000 \text{ g} = 10^3 \text{ g}\).
- Therefore, we convert:
\[ 9.1 \times 10^{-31} \text{ kg} \times 10^3 \text{ g/kg} = 9.1 \times 10^{-28} \text{ g} \]
- Thus, the first statement is **correct**.

### Step 2: Analyze the second statement
**Statement:** The mass of an electron increases with the increase in velocity.

**Solution:**
- The relativistic mass of an electron is given by the formula:
\[ m = m_0 \cdot \frac{1}{\sqrt{1 - \frac{v^2}{c^2}}} \]
where \(m_0\) is the rest mass, \(v\) is the velocity, and \(c\) is the speed of light.
- As \(v\) increases, \(\frac{v^2}{c^2}\) increases, making the denominator smaller, which in turn increases the mass \(m\).
- Therefore, the second statement is **correct**.

### Step 3: Analyze the third statement
**Statement:** The molar mass of an electron is \(5.48 \times 10^{-4}\) g/mol.

**Solution:**
- The molar mass is calculated using the formula:
\[ \text{Molar mass} = \text{mass of electron} \times \text{Avogadro's number} \]
- Given:
- Mass of electron = \(9.1 \times 10^{-28}\) g
- Avogadro's number = \(6.022 \times 10^{23} \text{ mol}^{-1}\)
- Calculation:
\[ \text{Molar mass} = 9.1 \times 10^{-28} \text{ g} \times 6.022 \times 10^{23} \text{ mol}^{-1} \approx 5.48 \times 10^{-4} \text{ g/mol} \]
- Thus, the third statement is **correct**.

### Step 4: Analyze the fourth statement
**Statement:** The charge-to-mass ratio of an electron is \(1.7 \times 10^{8}\) C/g.

**Solution:**
- The charge-to-mass ratio is calculated as:
\[ \frac{e}{m} = \frac{\text{Charge of electron}}{\text{Mass of electron}} \]
- Given:
- Charge of electron = \(1.6 \times 10^{-19} \text{ C}\)
- Mass of electron = \(9.1 \times 10^{-28} \text{ g}\)
- Calculation:
\[ \frac{e}{m} = \frac{1.6 \times 10^{-19} \text{ C}}{9.1 \times 10^{-28} \text{ g}} \approx 1.7 \times 10^{8} \text{ C/g} \]
- Thus, the fourth statement is **correct**.

### Conclusion
All four statements about the electron are **correct**.

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