If the energy of electron in H atom is given by expression `- 1312 n^(2) kJ "mole"^(-1)` then the energy required to excited the elcxtron from ground state to second orbit is

Options

A. `328 kJ`
B. `656 kJ`
C. `984 kJ`
D. `312 kJ`

Explanation

To find the energy required to excite the electron in a hydrogen atom from the ground state (n=1) to the second orbit (n=2), we can follow these steps:

### Step 1: Calculate the energy of the ground state (n=1)
The formula for the energy of an electron in a hydrogen atom is given by:

\[ E_n = -\frac{1312}{n^2} \text{ kJ/mole} \]

For the ground state (n=1):

\[ E_1 = -\frac{1312}{1^2} = -1312 \text{ kJ/mole} \]

### Step 2: Calculate the energy of the second orbit (n=2)
Now, we calculate the energy for the second orbit (n=2):

\[ E_2 = -\frac{1312}{2^2} = -\frac{1312}{4} = -328 \text{ kJ/mole} \]

### Step 3: Calculate the energy difference (excitation energy)
The energy required to excite the electron from the ground state to the second orbit is the difference between the energy of the second orbit and the energy of the ground state:

\[ \Delta E = E_2 - E_1 \]

Substituting the values we calculated:

\[ \Delta E = -328 - (-1312) = -328 + 1312 = 984 \text{ kJ/mole} \]

### Conclusion
The energy required to excite the electron from the ground state to the second orbit is:

\[ \Delta E = 984 \text{ kJ/mole} \]

Thus, the correct option is **C, 984 kJ/mole**.

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