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

Options

A. `2.4xx10^(7)Ckg^(-1)`
B. `4.8xx10^(7)Ckg^(-1)`
C. `19.2xx10^(7)Ckg^(-1)`
D. `38.4xx10^(7)Ckg^(-1)`

Answer

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

### Step 1: Understand the specific charge of a proton
The specific charge of a proton is given as \( 9.6 \times 10^7 \, \text{C kg}^{-1} \). The specific charge is defined as the charge of the particle divided by its mass.

### Step 2: Define the alpha particle
An alpha particle is essentially a doubly ionized helium atom, represented as \( \text{He}^{2+} \). It consists of 2 protons and 2 neutrons.

### Step 3: Determine the charge of the alpha particle
The charge of an alpha particle is the sum of the charges of its protons. Since each proton has a charge of \( +e \) (where \( e \) is the elementary charge), the total charge of the alpha particle is:
\[ \text{Charge of alpha particle} = +2e \]

### Step 4: Determine the mass of the alpha particle
The mass of an alpha particle is the sum of the masses of its protons and neutrons. Since it has 2 protons and 2 neutrons, its mass can be approximated as:
\[ \text{Mass of alpha particle} = 2 \times m_p + 2 \times m_n \approx 4m_p \]
(where \( m_p \) is the mass of a proton and \( m_n \) is the mass of a neutron, and we can assume \( m_n \approx m_p \) for simplicity).

### Step 5: Calculate the specific charge of the alpha particle
The specific charge of the alpha particle can be calculated using the formula:
\[ \text{Specific charge of alpha particle} = \frac{\text{Charge of alpha particle}}{\text{Mass of alpha particle}} = \frac{+2e}{4m_p} = \frac{1}{2} \cdot \frac{e}{m_p} \]
This shows that the specific charge of the alpha particle is half that of the proton.

### Step 6: Substitute the specific charge of the proton
Now, we can substitute the specific charge of the proton into our equation:
\[ \text{Specific charge of alpha particle} = \frac{1}{2} \cdot (9.6 \times 10^7 \, \text{C kg}^{-1}) = 4.8 \times 10^7 \, \text{C kg}^{-1} \]

### Conclusion
Thus, the specific charge of the alpha particle is:
\[ \text{Specific charge of alpha particle} = 4.8 \times 10^7 \, \text{C kg}^{-1} \]