An electron in Bohr's hydrogen atom has an energy of -3.4 eV. The angular momentum of the electron is

Options

A. `(h)/(pi)`
B. `(h)/(2pi)`
C. `(nh)/(2pi)`(n is an integer)
D. `(2h)/(pi)`

Explanation

To find the angular momentum of an electron in a hydrogen atom with a given energy of -3.4 eV, we can follow these steps:

### Step 1: Understand the energy formula in Bohr's model
In Bohr's model of the hydrogen atom, the energy of an electron in the nth orbit is given by the formula:
\[ E = -\frac{13.6 \, \text{eV}}{n^2} \]
where \( E \) is the energy of the electron and \( n \) is the principal quantum number (orbit number).

### Step 2: Set up the equation with the given energy
Given that the energy \( E = -3.4 \, \text{eV} \), we can set up the equation:
\[ -3.4 = -\frac{13.6}{n^2} \]

### Step 3: Solve for \( n^2 \)
Removing the negative signs from both sides gives:
\[ 3.4 = \frac{13.6}{n^2} \]
Now, rearranging the equation to solve for \( n^2 \):
\[ n^2 = \frac{13.6}{3.4} \]

### Step 4: Calculate \( n^2 \)
Calculating the right side:
\[ n^2 = \frac{13.6}{3.4} = 4 \]
Taking the square root gives:
\[ n = 2 \]

### Step 5: Use the angular momentum formula
According to Bohr's model, the angular momentum \( L \) of the electron in the nth orbit is given by:
\[ L = n \cdot \frac{h}{2\pi} \]
Substituting the value of \( n \):
\[ L = 2 \cdot \frac{h}{2\pi} \]

### Step 6: Simplify the expression
Simplifying the expression:
\[ L = \frac{h}{\pi} \]

### Final Answer
Thus, the angular momentum of the electron is:
\[ L = \frac{h}{\pi} \]

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