The energy of an electron in the 3rd orbit of an atom is `-E`. The energy of an electron in the first orbit will be

Options

A. `-3E`
B. `-E//3`
C. `-E//9`
D. `-9E`

Explanation

To find the energy of an electron in the first orbit when the energy in the third orbit is given as \(-E\), we can use the relationship between the energy levels of an electron in different orbits of an atom.

### Step-by-Step Solution:

1. **Understanding the Energy Relationship**:
The energy of an electron in the nth orbit is given by the formula:
\[ E_n \propto -\frac{1}{n^2} \]
This means that the energy is inversely proportional to the square of the principal quantum number \(n\).

2. **Setting Up the Equation**:
Given that the energy in the third orbit (\(E_3\)) is \(-E\), we can express this as:
\[ E_3 = -E \]
We need to find the energy in the first orbit (\(E_1\)).

3. **Using the Proportionality**:
From the proportionality, we can write:
\[ \frac{E_1}{E_3} = \frac{-\frac{1}{1^2}}{-\frac{1}{3^2}} = \frac{1}{\frac{1}{9}} = 9 \]
This means:
\[ E_1 = 9 \cdot E_3 \]

4. **Substituting the Value of \(E_3\)**:
Now substitute \(E_3 = -E\) into the equation:
\[ E_1 = 9 \cdot (-E) = -9E \]

5. **Conclusion**:
Therefore, the energy of an electron in the first orbit is:
\[ E_1 = -9E \]

### Final Answer:
The energy of an electron in the first orbit will be \(-9E\).