The specific charge of a proton is `9.6xx10^(7)"C kg"^(-1)`.
The specific charge of an alpha particle will be

Options

A. `9.6xx10^(7)"C kg"^(-1)`
B. `19.2xx10^(7)"C kg"^(-1)`
C. `4.8xx10^(7)"C kg"^(-1)`
D. `2.4xx10^(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 \( \frac{E}{m} = 9.6 \times 10^7 \, \text{C kg}^{-1} \), where \( E \) is the charge and \( m \) is the mass.

### Step 2: Determine the charge and mass of an alpha particle
An alpha particle, denoted as \( \alpha \) or \( ^4He^{2+} \), consists of 2 protons and 2 neutrons. Therefore:
- The charge of an alpha particle \( E_{\alpha} \) is \( 2 \times E_{p} \) (where \( E_{p} \) is the charge of a proton).
- The mass of an alpha particle \( m_{\alpha} \) is \( 4 \times m_{p} \) (where \( m_{p} \) is the mass of a proton).

### Step 3: Write the specific charge formula for the alpha particle
The specific charge of the alpha particle can be expressed as:
\[ \frac{E_{\alpha}}{m_{\alpha}} = \frac{2E_{p}}{4m_{p}} = \frac{1}{2} \cdot \frac{E_{p}}{m_{p}} \]

### Step 4: Substitute the known specific charge of the proton
Now, substituting the specific charge of the proton into the equation:
\[ \frac{E_{\alpha}}{m_{\alpha}} = \frac{1}{2} \cdot 9.6 \times 10^7 \, \text{C kg}^{-1} \]

### Step 5: Calculate the specific charge of the alpha particle
Calculating this gives:
\[ \frac{E_{\alpha}}{m_{\alpha}} = 4.8 \times 10^7 \, \text{C kg}^{-1} \]

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

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