The energy required by electrons, present in the first Bohr orbit of hydrogen atom to J $$ mol^{-1}C $$ be excited to second Bohr orbit is ______ .
Given $$ R_{H}=2.18\times 10^{-11} $$

Find the energy required (in J/mol) to excite electrons from the first to second Bohr orbit of hydrogen.

$$E_n = -\frac{R_H}{n^2}$$

where $$R_H = 2.18 \times 10^{-18}$$ J (the Rydberg energy constant for hydrogen).

$$\Delta E = E_2 - E_1 = -\frac{R_H}{4} - \left(-\frac{R_H}{1}\right) = R_H\left(1 - \frac{1}{4}\right) = \frac{3}{4}R_H$$

$$\Delta E = \frac{3}{4} \times 2.18 \times 10^{-18} = 1.635 \times 10^{-18} \text{ J per atom}$$

Multiply by Avogadro's number $$N_A = 6.022 \times 10^{23}$$:

$$\Delta E_{\text{mol}} = 1.635 \times 10^{-18} \times 6.022 \times 10^{23}$$

$$= 1.635 \times 6.022 \times 10^{5} = 9.846 \times 10^{5} \approx 9.835 \times 10^5 \text{ J/mol}$$

The correct answer is Option (3): $$9.835 \times 10^5$$.