If the radius of 2nd Bohr orbit of hydrogen atom is r2. The radius of third Bohr orbit will be

Problem : If the radius of 2nd Bohr orbit of hydrogen atom is r2. The radius of third Bohr orbit will be

(A) $\large \frac{4}{9}r_2$

(B) $\large 4 r_2$

(C) $\large \frac{9}{4}r_2$

(D) $\large 9 r_2$

Ans: (C)

Sol: $\large r_n = \frac{n^2 h^2}{4\pi^2 m K Z e^2} $

$\large r_n \propto n^2$

$\large \frac{r_2}{r_3} = \frac{2^2}{3^2} $

$\large r_3 = \frac{9}{4}r_2$

What transition in the hydrogen spectrum would have the same wavelength…

Problem : What transition in the hydrogen spectrum would have the same wavelength as the Balmer transition, n = 4 to n = 2 in the He+ spectrum.

(A) n = 4 to n = 2

(B) n = 3 to n = 2

(C) n = 3 to n = 1

(D) n = 2 to n = 1

Ans: (D)

Solution: $\large \frac{1}{\lambda} = (\frac{1}{2^2} – \frac{1}{4^2}) = \frac{3}{4}R$

In H-spectrum for the same λ as Z = 1, n1 = 1, n2 = 2