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

Options

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

Explanation

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

### Step 1: Calculate the specific charge (e/m) for the electron.
The specific charge for an electron is given by the formula:

\[ \frac{e}{m} = \frac{\text{Charge of electron}}{\text{Mass of electron}} \]

The charge of an electron (e) is approximately \(1.6 \times 10^{-19}\) coulombs, and the mass of an electron (m) is approximately \(9.1 \times 10^{-31}\) kg.

Substituting these values:

\[ \frac{e}{m} \text{ (electron)} = \frac{1.6 \times 10^{-19}}{9.1 \times 10^{-31}} \text{ C/kg} \]

### Step 2: Calculate the specific charge (e/m) for the alpha particle.
An alpha particle consists of 2 protons and 2 neutrons, hence it has a charge of:

\[ \text{Charge of alpha particle} = 2 \times \text{Charge of proton} = 2 \times 1.6 \times 10^{-19} \text{ C} \]

The mass of an alpha particle is approximately 4 times the mass of a proton, which is about \(4 \times 1.6 \times 10^{-27}\) kg.

Thus, the specific charge for the alpha particle is:

\[ \frac{e}{m} \text{ (alpha particle)} = \frac{2 \times 1.6 \times 10^{-19}}{4 \times 1.6 \times 10^{-27}} \text{ C/kg} \]

### Step 3: Calculate the ratio of the specific charges (e/m) of the electron and alpha particle.
Now, we can find the ratio of the specific charges:

\[ \text{Ratio} = \frac{\frac{e}{m} \text{ (electron)}}{\frac{e}{m} \text{ (alpha particle)}} \]

Substituting the values we calculated:

\[ \text{Ratio} = \frac{\frac{1.6 \times 10^{-19}}{9.1 \times 10^{-31}}}{\frac{2 \times 1.6 \times 10^{-19}}{4 \times 1.6 \times 10^{-27}}} \]

### Step 4: Simplify the ratio.
This simplifies to:

\[ \text{Ratio} = \frac{1.6 \times 10^{-19} \times 4 \times 1.6 \times 10^{-27}}{2 \times 1.6 \times 10^{-19} \times 9.1 \times 10^{-31}} \]

Cancelling \(1.6 \times 10^{-19}\) from the numerator and denominator:

\[ \text{Ratio} = \frac{4 \times 10^{-27}}{2 \times 9.1 \times 10^{-31}} = \frac{4}{2 \times 9.1} \times 10^{4} = \frac{2}{9.1} \times 10^{4} \]

Calculating this gives approximately:

\[ \text{Ratio} \approx 3.5 \times 10^{3} \]

### Conclusion
The ratio of the specific charge values of an electron to an alpha particle is approximately \(3516\).