The ratio of specific charge of an `alpha-` particle to that of a proton is

Options

A. `2:1`
B. `1:1`
C. `1:2`
D. `1:3`

Answer

To find the ratio of the specific charge of an alpha particle to that of a proton, we will follow these steps:

### Step 1: Define Specific Charge
The specific charge (SC) is defined as the charge (q) divided by the mass (m) of the particle. Mathematically, it is represented as:
\[ \text{Specific Charge (SC)} = \frac{q}{m} \]

### Step 2: Identify the Charge and Mass of the Proton
- The charge of a proton (\(q_p\)) is \(+1e\) (where \(e\) is the elementary charge, approximately \(1.6 \times 10^{-19} \, \text{C}\)).
- The mass of a proton (\(m_p\)) is approximately \(1 \, \text{amu}\) (atomic mass unit).

### Step 3: Calculate the Specific Charge of the Proton
Using the values from Step 2:
\[ \text{SC}_{\text{proton}} = \frac{q_p}{m_p} = \frac{1e}{1 \, \text{amu}} \]

### Step 4: Identify the Charge and Mass of the Alpha Particle
- An alpha particle consists of 2 protons and 2 neutrons. Therefore, its charge (\(q_{\alpha}\)) is \(+2e\).
- The mass of an alpha particle (\(m_{\alpha}\)) is approximately \(4 \, \text{amu}\) (since it has 2 protons and 2 neutrons).

### Step 5: Calculate the Specific Charge of the Alpha Particle
Using the values from Step 4:
\[ \text{SC}_{\alpha} = \frac{q_{\alpha}}{m_{\alpha}} = \frac{2e}{4 \, \text{amu}} = \frac{1e}{2 \, \text{amu}} \]

### Step 6: Calculate the Ratio of Specific Charges
Now, we can find the ratio of the specific charge of the alpha particle to that of the proton:
\[ \text{Ratio} = \frac{\text{SC}_{\alpha}}{\text{SC}_{\text{proton}}} = \frac{\frac{1e}{2 \, \text{amu}}}{\frac{1e}{1 \, \text{amu}}} \]

### Step 7: Simplify the Ratio
This simplifies to:
\[ \text{Ratio} = \frac{1e}{2 \, \text{amu}} \times \frac{1 \, \text{amu}}{1e} = \frac{1}{2} \]

### Step 8: Final Answer
Thus, the ratio of the specific charge of an alpha particle to that of a proton is:
\[ \text{Ratio} = 1 : 2 \]