The binding energy of the electron in the third orbit is 1.51 eV. Its. P.E. in the same orbit is

Options

A. `-1.51` eV
B. `-3.4` eV
C. `-3.02` eV
D. 3.02 eV

Explanation

To find the potential energy (P.E.) of the electron in the third orbit, we can follow these steps:

### Step 1: Understand the relationship between binding energy and total energy
The binding energy (B.E.) of an electron in an orbit is defined as the energy required to remove the electron from that orbit to infinity. It is given that the binding energy of the electron in the third orbit is 1.51 eV.

### Step 2: Relate binding energy to total energy
The total energy (E) of an electron in an orbit is given by the negative of the binding energy. Therefore, we can express this as:
\[ E = -B.E. \]
Substituting the given binding energy:
\[ E = -1.51 \, \text{eV} \]

### Step 3: Use the relationship between total energy and potential energy
In atomic physics, the total energy (E) of an electron in an orbit is related to its potential energy (P.E.) by the formula:
\[ E = \frac{P.E.}{2} \]
This means that the potential energy is twice the total energy:
\[ P.E. = 2 \times E \]

### Step 4: Calculate the potential energy
Now, substituting the total energy we found:
\[ P.E. = 2 \times (-1.51 \, \text{eV}) \]
\[ P.E. = -3.02 \, \text{eV} \]

### Conclusion
The potential energy of the electron in the third orbit is \(-3.02 \, \text{eV}\).

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