According to Bohr's theory the possible value of angular momentum of an electron orbiting in hydrogen atom is

Options

A. `(4h)/(3π)`
B. `h/π`
C. `(4h)/(5π)`
D. both (1) & (3)

Answer

To solve the problem of finding the possible value of angular momentum of an electron orbiting in a hydrogen atom according to Bohr's theory, we can follow these steps:

### Step 1: Understand Bohr's Model
Bohr's model states that electrons move in fixed orbits around the nucleus and that the angular momentum of an electron in these orbits is quantized.

### Step 2: Write the Formula for Angular Momentum
According to Bohr's theory, the angular momentum \( L \) of an electron in the \( n \)-th orbit is given by the formula:
\[ L = n \frac{h}{2\pi} \]
where:
- \( L \) is the angular momentum,
- \( n \) is the principal quantum number (the orbit number),
- \( h \) is Planck's constant.

### Step 3: Determine the Value of \( n \)
For the hydrogen atom, the ionization energy is given as 3.4 eV. The energy of an electron in the \( n \)-th orbit is given by:
\[ E_n = -\frac{13.6}{n^2} \text{ eV} \]
Setting this equal to the ionization energy:
\[ 3.4 = -\frac{13.6}{n^2} \]
We can rearrange this equation to find \( n^2 \):
\[ n^2 = \frac{13.6}{3.4} \]
Calculating this gives:
\[ n^2 = 4 \implies n = 2 \]

### Step 4: Substitute \( n \) into the Angular Momentum Formula
Now that we have \( n = 2 \), we can substitute this value into the angular momentum formula:
\[ L = 2 \frac{h}{2\pi} = \frac{2h}{2\pi} = \frac{h}{\pi} \]

### Step 5: Conclusion
Thus, the possible value of angular momentum of an electron orbiting in a hydrogen atom according to Bohr's theory is:
\[ L = \frac{h}{\pi} \]

### Final Answer
The possible value of angular momentum of an electron orbiting in a hydrogen atom is \( \frac{h}{\pi} \).

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