If electron of hydrogen atom is replaced by another particle of same charge but of double mass then:

Options

A. Radii of orbits will increase
B. Ionisation energy will increase
C. Velocity of new particle will be more
D. Energy gap between two levels will be doubled

Answer

To solve the question regarding the effects of replacing the electron in a hydrogen atom with a particle of the same charge but double the mass, we can analyze the situation step by step.

### Step-by-Step Solution:

1. **Understanding the Hydrogen Atom Structure**:
- A hydrogen atom consists of one proton in the nucleus and one electron in orbit around it. The electron has a certain mass (denoted as \( m_e \)) and charge (\( -e \)).

2. **Replacing the Electron**:
- We replace the electron with another particle that has the same charge (\( -e \)) but double the mass (\( 2m_e \)).

3. **Effect on the Radius of Orbit**:
- The radius of the nth orbit in a hydrogen atom is given by the formula:
\[ r_n \propto \frac{1}{m_e} \]
- If we double the mass of the particle, the new radius \( r'_n \) becomes:
\[ r'_n = \frac{r_n}{2} \]
- Thus, the radius of the orbit decreases.

4. **Effect on Ionization Energy**:
- Ionization energy is directly proportional to the mass of the electron:
\[ \text{Ionization Energy} \propto m_e \]
- If the mass is doubled, the new ionization energy \( E'_i \) becomes:
\[ E'_i = 2E_i \]
- Therefore, the ionization energy increases.

5. **Effect on Velocity of the Particle**:
- The velocity of an electron in the nth orbit is given by:
\[ v_n \propto \frac{1}{\sqrt{m_e}} \]
- If the mass is doubled, the new velocity \( v' \) becomes:
\[ v' = \frac{v_n}{\sqrt{2}} \]
- Hence, the velocity of the particle decreases.

6. **Effect on Energy Gap Between Levels**:
- The energy gap \( \Delta E \) between two energy levels is also proportional to the mass of the electron:
\[ \Delta E \propto m_e \]
- If the mass is doubled, the new energy gap \( \Delta E' \) becomes:
\[ \Delta E' = 2\Delta E \]
- Thus, the energy gap between levels doubles.

### Conclusion:
Based on the analysis:
- The radius of the orbit decreases (not increases).
- The ionization energy increases.
- The velocity of the particle decreases (not increases).
- The energy gap between levels doubles.

### Final Answers:
- **Correct Options**: B (Ionization energy will increase) and D (Energy gap between two levels will be doubled).
- **Incorrect Options**: A (Radii of orbit will increase) and C (Velocity of new particle will be more).