For an electron in the third orbit Bohr hydrogen atom, the moment of linear momentum is

Options

A. `npi`
B. `3pih`
C. `(3h)/(2pi)`
D. `h/pi`

Answer

To find the moment of linear momentum (angular momentum) for an electron in the third orbit of a Bohr hydrogen atom, we can follow these steps:

### Step 1: Understand the formula for angular momentum in Bohr's model
According to Bohr's theory, the angular momentum (L) of an electron in the nth 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 2: Identify the value of n
For the electron in the third orbit, the principal quantum number \( n \) is:
\[ n = 3 \]

### Step 3: Substitute the value of n into the formula
Now, we substitute \( n = 3 \) into the angular momentum formula:
\[ L = 3 \frac{h}{2\pi} \]

### Step 4: Simplify the expression
This gives us the angular momentum for the electron in the third orbit:
\[ L = \frac{3h}{2\pi} \]

### Step 5: Conclusion
Thus, the moment of linear momentum (angular momentum) for an electron in the third orbit of a Bohr hydrogen atom is:
\[ L = \frac{3h}{2\pi} \]

### Final Answer
The correct answer is \( \frac{3h}{2\pi} \).

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