Question

The energy required by electrons, present in the first Bohr orbit of hydrogen atom, to be excited to second Bohr orbit is ________ J mol\(^{-1}\). Given: \(R_H = 2.18 \times 10^{-11}\) ergs.

• A. \(9.835 \times 10^{12}\)
• B. \(9.835 \times 10^{5}\)
• C. \(1.635 \times 10^{-11}\)
• D. \(1.635 \times 10^{-18}\)

Hint:

Energy required for excitation equals the difference between energies of final and initial Bohr orbits.

Answer 1

The Correct Option is C

Step 1: Write the energy expression for Bohr orbits.
Energy of an electron in the \(n^{th}\) orbit is: \[ E_n = -\frac{R_H}{n^2} \] Step 2: Calculate energy difference between first and second orbits.
\[ E_1 = -R_H,\quad E_2 = -\frac{R_H}{4} \] \[ \Delta E = E_2 - E_1 = \left(-\frac{R_H}{4}\right) - (-R_H) = \frac{3R_H}{4} \] Step 3: Substitute the given value.
\[ \Delta E = \frac{3}{4}\times 2.18 \times 10^{-11} = 1.635 \times 10^{-11} \] Final Answer: \[ \boxed{1.635 \times 10^{-11}\ \text{J mol}^{-1}} \]