If the energy of electron in H atom is given by expression, `-1312//n^(2)"k J mol"^(-1)`, then the energy required to excite the electron from ground state to second orbit is:

Options

A. 328kJ/mol
B. 656 kJ/mol
C. 984 kJ/mol
D. 1312 kJ/mol

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: Write the energy expression for the hydrogen atom
The energy of an electron in a hydrogen atom is given by the formula:
\[ E_n = -\frac{1312}{n^2} \text{ kJ/mol} \]
where \( n \) is the principal quantum number.

### Step 2: Calculate the energy for the ground state (n=1)
Substituting \( n = 1 \) into the energy formula:
\[ E_1 = -\frac{1312}{1^2} = -1312 \text{ kJ/mol} \]

### Step 3: Calculate the energy for the second orbit (n=2)
Now, substituting \( n = 2 \) into the energy formula:
\[ E_2 = -\frac{1312}{2^2} = -\frac{1312}{4} = -328 \text{ kJ/mol} \]

### Step 4: Calculate the energy difference (ΔE)
The energy required to excite the electron from the ground state to the second orbit is given by the difference in energy:
\[ \Delta E = E_2 - E_1 \]
Substituting the values we calculated:
\[ \Delta E = -328 - (-1312) = -328 + 1312 = 984 \text{ kJ/mol} \]

### Final Answer
The energy required to excite the electron from the ground state to the second orbit is:
\[ \Delta E = 984 \text{ kJ/mol} \]

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