The specific charge of a proton is `9.6 xx 10^7 C kg^-1`, then for and `alpha-"particles"` it will be.

Options

A. `2.4 xx 10^7 C kg^-1`
B. `4.8 xx 10^7 C kg^-1`
C. `19.2 xx 10^7 C kg^-1`
D. `38.4 xx 10^7 C kg^-1`

Explanation

To find the specific charge of an alpha particle, we can follow these steps:

### Step 1: Understand the specific charge of a proton
The specific charge of a proton is given as \( \frac{E}{m} = 9.6 \times 10^7 \, \text{C kg}^{-1} \).

### Step 2: Identify the charge and mass of an alpha particle
An alpha particle consists of 2 protons and 2 neutrons. Therefore:
- **Charge of an alpha particle**: Since it has 2 protons, the charge is \( 2 \times e \) (where \( e \) is the elementary charge, approximately \( 1.6 \times 10^{-19} \, \text{C} \)).
- **Mass of an alpha particle**: The mass of an alpha particle is approximately \( 4 \, m_p \) (where \( m_p \) is the mass of a proton).

### Step 3: Calculate the specific charge of the alpha particle
The specific charge \( \frac{E}{m} \) for the alpha particle can be calculated using the formula:
\[ \frac{E}{m} = \frac{2e}{4m_p} \]
This simplifies to:
\[ \frac{E}{m} = \frac{1}{2} \cdot \frac{e}{m_p} \]

### Step 4: Substitute the specific charge of a proton
We know the specific charge of a proton \( \frac{e}{m_p} \) is \( 9.6 \times 10^7 \, \text{C kg}^{-1} \). Therefore:
\[ \frac{E}{m} = \frac{1}{2} \cdot 9.6 \times 10^7 \, \text{C kg}^{-1} \]

### Step 5: Perform the calculation
Calculating this gives:
\[ \frac{E}{m} = 4.8 \times 10^7 \, \text{C kg}^{-1} \]

### Conclusion
The specific charge of an alpha particle is \( 4.8 \times 10^7 \, \text{C kg}^{-1} \).

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