Q. The energy level diagram for an hydrogen like atom is shown in the figure. The radius of its first Bohr orbit is
A) $0.265\ \mathring{\mathrm{A}}$
B) $0.53\ \mathring{\mathrm{A}}$
C) $0.132\ \mathring{\mathrm{A}}$
D) None of these
Explanation
(a) We know that $E_{n} = - 13.6\frac{Z^{2}}{n^{2}} = eV$ and $r_{n} = 0.53\frac{n^{2}}{Z}(\mathring{\mathrm{A}})$
Here for $n = 1,E_{1} = - 54.4\ eV$
Therefore $- 54.4 = - 13.6\frac{Z^{2}}{1^{2}} \Rightarrow Z = 2$
Hence radius of first Bohr orbit $r = \frac{0.53(1)^{2}}{2} = 0.265\ \mathring{\mathrm{A}}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.