The ratio of angular momentum of electron in two successive orbit is a `(a gt1)` and their difference is b . Then `a/b` is equal to `

Options

A. `n/(n+1)`
B. `(n+1)/n`
C. `(n+1)/n.h/(2pi)`
D. `((n+1)/n).(2pi)/h`

Answer

To solve the problem, we need to find the ratio \( \frac{a}{b} \) where \( a \) is the ratio of angular momentum of an electron in two successive orbits and \( b \) is the difference in their angular momentum.

### Step-by-Step Solution:

1. **Identify Angular Momentum Formula**:
The angular momentum \( L \) of an electron in an orbit is given by:
\[ L = n \frac{h}{2\pi} \]
where \( n \) is the principal quantum number and \( h \) is Planck's constant.

2. **Angular Momentum for Two Successive Orbits**:
For the orbit with principal quantum number \( n \):
\[ L_n = n \frac{h}{2\pi} \]
For the next orbit with principal quantum number \( n + 1 \):
\[ L_{n+1} = (n + 1) \frac{h}{2\pi} \]

3. **Calculate the Ratio \( a \)**:
The ratio of angular momentum in two successive orbits is:
\[ a = \frac{L_{n+1}}{L_n} = \frac{(n + 1) \frac{h}{2\pi}}{n \frac{h}{2\pi}} = \frac{n + 1}{n} \]

4. **Calculate the Difference \( b \)**:
The difference in angular momentum between the two orbits is:
\[ b = L_{n+1} - L_n = \left( (n + 1) \frac{h}{2\pi} - n \frac{h}{2\pi} \right) = \frac{h}{2\pi} \]

5. **Find the Ratio \( \frac{a}{b} \)**:
Now we can find the ratio \( \frac{a}{b} \):
\[ \frac{a}{b} = \frac{\frac{n + 1}{n}}{\frac{h}{2\pi}} = \frac{(n + 1) \cdot 2\pi}{n \cdot h} \]

### Final Answer:
Thus, the value of \( \frac{a}{b} \) is:
\[ \frac{a}{b} = \frac{(n + 1) \cdot 2\pi}{n \cdot h} \]