Which of the following shows an increasing value of `e//m`?

Options

A. `n lt alpha lt p lt e`
B. `n lt p lt alpha lt e`
C. `n lt p lt e lt alpha`
D. ` p lt n lt alpha lt e`

Explanation

To determine which of the following shows an increasing value of \( \frac{e}{m} \) (the charge-to-mass ratio), we need to calculate the \( \frac{e}{m} \) values for each of the particles mentioned: proton, neutron, alpha particle, and electron.

### Step-by-Step Solution:

1. **Identify the particles and their charges and masses**:
- **Proton (p)**:
- Charge (\( e \)) = +1 (in units of elementary charge)
- Mass (\( m \)) = 1 amu
- **Neutron (n)**:
- Charge (\( e \)) = 0
- Mass (\( m \)) = 1 amu
- **Alpha particle (α)**:
- Charge (\( e \)) = +2 (since it is \( \text{He}^{2+} \))
- Mass (\( m \)) = 4 amu
- **Electron (e)**:
- Charge (\( e \)) = -1 (in units of elementary charge)
- Mass (\( m \)) = \( \frac{1}{1837} \) amu

2. **Calculate the \( \frac{e}{m} \) for each particle**:
- For **Proton**:
\[ \frac{e}{m} = \frac{1}{1} = 1 \]
- For **Neutron**:
\[ \frac{e}{m} = \frac{0}{1} = 0 \]
- For **Alpha particle**:
\[ \frac{e}{m} = \frac{2}{4} = 0.5 \]
- For **Electron**:
\[ \frac{e}{m} = \frac{1}{\frac{1}{1837}} = 1837 \]

3. **List the \( \frac{e}{m} \) values in order**:
- Neutron: \( 0 \)
- Alpha particle: \( 0.5 \)
- Proton: \( 1 \)
- Electron: \( 1837 \)

4. **Determine the increasing order of \( \frac{e}{m} \)**:
- The increasing order is: Neutron < Alpha particle < Proton < Electron.

5. **Conclusion**:
- The order of increasing \( \frac{e}{m} \) is Neutron < Alpha particle < Proton < Electron.

### Final Answer:
The increasing order of \( \frac{e}{m} \) is: Neutron < Alpha particle < Proton < Electron.