Question

Which of the following statements are correct? (only correct)
I) The energy of hydrogen atom in its ground state is -13.6 eV.
II) On the basis of Bohr's model, the radius of the 3$^{rd}$ orbit of hydrogen atom is 158.7 pm.
III) The order of radius of the first orbit of H, He$^+$, Li$^{2+}$ and Be$^{3+}$ is H > He$^+$ > Li$^{2+}$ > Be$^{3+}$

• A. II & III only
• B. I & III only
• C. I & II only
• D. I, II, III

Hint:

Remember the Bohr radius formula and that radius inversely depends on nuclear charge $Z$ for hydrogen-like ions.

Answer 1

The Correct Option is B

I) The energy of hydrogen atom in ground state is correctly -13.6 eV, according to Bohr's theory.
II) Using Bohr's radius formula, \( r_n = n^2 a_0 \), where \( a_0 = 0.529 \) Å, for \( n=3 \), the radius is \( 9 \times 0.529 = 4.761 \) Å = 476.1 pm, not 158.7 pm. So II is incorrect.
III) For hydrogen-like ions, the radius decreases as nuclear charge \( Z \) increases. Hence, the radius order is \( {H} (Z=1) >{He}^+ (Z=2) > {Li}^{2+} (Z=3) >{Be}^{3+} (Z=4) \). Statement III is correct.