According to Bohrr model of hydrogen atom, only those orbit are permissible which satisfy the condition

Options

A. mv=nh
B. `(mv^(2))/(r)=n((h)/(2pi))`
C. `mvr=n ((h)/(2pi))`
D. `mvr^(2)=n((h)/(2pi))`

Explanation

To solve the question regarding the permissible orbits in the Bohr model of the hydrogen atom, we follow these steps:

### Step-by-Step Solution:

1. **Understanding the Bohr Model**:
- The Bohr model of the hydrogen atom states that electrons move in fixed orbits around the nucleus and that these orbits are quantized.

2. **Angular Momentum Quantization**:
- According to Bohr's theory, the angular momentum (L) of an electron in a hydrogen atom is quantized. This means that it can only take on certain discrete values.

3. **Expression for Angular Momentum**:
- The angular momentum (L) of an electron in orbit is given by the formula:
\[ L = mvr \]
where:
- \( m \) is the mass of the electron,
- \( v \) is the velocity of the electron,
- \( r \) is the radius of the orbit.

4. **Quantization Condition**:
- Bohr postulated that the angular momentum is quantized and can be expressed as:
\[ L = n \frac{h}{2\pi} \]
where:
- \( n \) is a positive integer (principal quantum number),
- \( h \) is Planck's constant.

5. **Setting the Equations Equal**:
- By equating the two expressions for angular momentum, we have:
\[ mvr = n \frac{h}{2\pi} \]

6. **Conclusion**:
- Thus, the condition that must be satisfied for permissible orbits in the hydrogen atom according to the Bohr model is:
\[ mv r = n \frac{h}{2\pi} \]
- Therefore, the correct option is:
\[ \text{Option 3: } mv r = \frac{nh}{2\pi} \]