The total energy of an electron revolving in the second orbit of a hydrogen atom is

Options

A. `-13.6 eV`
B. `-1.51 eV`
C. `-3.4 eV`
D. Zero

Answer

To find the total energy of an electron revolving in the second orbit of a hydrogen atom, we can follow these steps:

### Step 1: Understand the Formula
The total energy \( E \) of an electron in the nth orbit of a hydrogen atom is given by the formula:
\[ E = -\frac{13.6 \, \text{eV} \cdot Z^2}{n^2} \]
where:
- \( E \) is the total energy,
- \( Z \) is the atomic number (for hydrogen, \( Z = 1 \)),
- \( n \) is the principal quantum number (for the second orbit, \( n = 2 \)).

### Step 2: Substitute Values
Since we are dealing with hydrogen, we substitute \( Z = 1 \) and \( n = 2 \) into the formula:
\[ E = -\frac{13.6 \, \text{eV} \cdot (1)^2}{(2)^2} \]

### Step 3: Calculate the Denominator
Calculate \( (2)^2 \):
\[ (2)^2 = 4 \]

### Step 4: Substitute and Simplify
Now substitute back into the equation:
\[ E = -\frac{13.6 \, \text{eV}}{4} \]

### Step 5: Perform the Division
Now divide \( 13.6 \, \text{eV} \) by \( 4 \):
\[ E = -3.4 \, \text{eV} \]

### Conclusion
The total energy of an electron revolving in the second orbit of a hydrogen atom is:
\[ E = -3.4 \, \text{eV} \]

### Final Answer
The answer is \(-3.4 \, \text{eV}\).

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