The ration of the `"e//m"` (specific charge) values of an electron and an `alpha-"particle"` is

Options

A. `2 : 1`
B. `1 : 1`
C. `1 : 2`
D. None of these

Explanation

To find the ratio of the specific charge (e/m) values of an electron and an alpha particle, we can follow these steps:

### Step 1: Determine the charge of the electron and alpha particle
- The charge of an electron (e) is \( -1.6 \times 10^{-19} \) coulombs.
- The charge of an alpha particle is \( +2e \) (since it consists of 2 protons and 2 neutrons), which equals \( +3.2 \times 10^{-19} \) coulombs.

### Step 2: Determine the mass of the electron and alpha particle
- The mass of the electron (m_e) is \( 9.1 \times 10^{-31} \) kg.
- The mass of an alpha particle (m_α) is approximately 4 times the mass of a proton. The mass of a proton is about \( 1.67 \times 10^{-27} \) kg, so:
\[ m_α = 4 \times 1.67 \times 10^{-27} \text{ kg} = 6.68 \times 10^{-27} \text{ kg} \]

### Step 3: Calculate the specific charge (e/m) for both particles
- For the electron:
\[ \frac{e}{m_e} = \frac{-1.6 \times 10^{-19}}{9.1 \times 10^{-31}} \text{ C/kg} \]
- For the alpha particle:
\[ \frac{e}{m_α} = \frac{+3.2 \times 10^{-19}}{6.68 \times 10^{-27}} \text{ C/kg} \]

### Step 4: Find the ratio of the specific charges
- The ratio of specific charges (e/m) of the electron to the alpha particle is:
\[ \text{Ratio} = \frac{\frac{e}{m_e}}{\frac{e}{m_α}} = \frac{-1.6 \times 10^{-19}/9.1 \times 10^{-31}}{3.2 \times 10^{-19}/6.68 \times 10^{-27}} \]

### Step 5: Simplify the ratio
- This simplifies to:
\[ \text{Ratio} = \frac{-1.6 \times 10^{-19} \times 6.68 \times 10^{-27}}{3.2 \times 10^{-19} \times 9.1 \times 10^{-31}} \]
- Further simplifying gives:
\[ \text{Ratio} = \frac{-1.6 \times 6.68}{3.2 \times 9.1} \times \frac{10^{-19} \times 10^{-27}}{10^{-19} \times 10^{-31}} = \frac{-1.6 \times 6.68}{3.2 \times 9.1} \times 10^{12} \]

### Step 6: Calculate the numerical value
- After calculating the numerical values, we find that:
\[ \text{Ratio} = \frac{-1.6 \times 6.68}{3.2 \times 9.1} \approx -\frac{10.688}{29.12} \approx -0.366 \]
- The negative sign indicates the charge nature, but we are interested in the magnitude for the ratio.

### Final Answer
The ratio of the specific charge values of an electron to an alpha particle is approximately \( 0.366 \).