The increasing order (lowest first) for the values of `e//m` (charge/mass) for electron `(e)`, proton `(p)`, neutron `(n)`, and alpha particle `(alpha)` is

Options

A. (a) `e`,`p`,`n`,`alpha`
B. (b) `n`,`p`,`e`,`alpha`
C. (c) `n`,`p`,`alpha`,`e`
D. (d) `n`,`alpha`,`p`,`e`

Answer

To determine the increasing order of the values of \( \frac{e}{m} \) (charge/mass) for an electron, proton, neutron, and alpha particle, we will analyze the charge and mass of each particle.

### Step-by-Step Solution:

1. **Identify the Charge and Mass of Each Particle:**
- **Electron (e):**
- Charge (\( q_e \)) = \(-1.6 \times 10^{-19} \) C
- Mass (\( m_e \)) = \( 9.11 \times 10^{-31} \) kg
- **Proton (p):**
- Charge (\( q_p \)) = \( +1.6 \times 10^{-19} \) C
- Mass (\( m_p \)) = \( 1.67 \times 10^{-27} \) kg
- **Neutron (n):**
- Charge (\( q_n \)) = \( 0 \) C
- Mass (\( m_n \)) = \( 1.67 \times 10^{-27} \) kg
- **Alpha Particle (α):**
- Charge (\( q_\alpha \)) = \( +3.2 \times 10^{-19} \) C (since it has 2 protons)
- Mass (\( m_\alpha \)) = \( 4 \times m_p \) (approximately \( 4 \times 1.67 \times 10^{-27} \) kg)

2. **Calculate \( \frac{q}{m} \) for Each Particle:**
- **Neutron:**
\[ \frac{q_n}{m_n} = \frac{0}{1.67 \times 10^{-27}} = 0 \]
- **Proton:**
\[ \frac{q_p}{m_p} = \frac{1.6 \times 10^{-19}}{1.67 \times 10^{-27}} \approx 9.58 \times 10^{7} \, \text{C/kg} \]
- **Electron:**
\[ \frac{q_e}{m_e} = \frac{-1.6 \times 10^{-19}}{9.11 \times 10^{-31}} \approx -1.76 \times 10^{11} \, \text{C/kg} \]
- **Alpha Particle:**
\[ \frac{q_\alpha}{m_\alpha} = \frac{3.2 \times 10^{-19}}{4 \times 1.67 \times 10^{-27}} \approx 4.80 \times 10^{7} \, \text{C/kg} \]

3. **Compare the Values:**
- Neutron: \( 0 \)
- Alpha Particle: \( \approx 4.80 \times 10^{7} \, \text{C/kg} \)
- Proton: \( \approx 9.58 \times 10^{7} \, \text{C/kg} \)
- Electron: \( \approx -1.76 \times 10^{11} \, \text{C/kg} \)

4. **Determine the Increasing Order:**
- The increasing order of \( \frac{e}{m} \) is:
- Neutron (0)
- Alpha Particle (\( \approx 4.80 \times 10^{7} \))
- Proton (\( \approx 9.58 \times 10^{7} \))
- Electron (\( \approx -1.76 \times 10^{11} \))

Thus, the final increasing order of \( \frac{e}{m} \) is:
**Neutron < Alpha Particle < Proton < Electron**