question_answer

According to Bohr theory the radius of electron orbit described by principal atomic number n and for atomic number Z is proportional:

A) \[{{Z}^{2}}{{n}^{2}}\]                                     

B) \[\frac{{{Z}^{2}}}{{{n}^{2}}}\]

C)  \[\frac{{{n}^{2}}}{Z}\]                                  

D) \[\frac{{{Z}^{2}}}{n}\]

Correct Answer: C

Solution :

                From Bohrs postulate the angular momentum of electron is                 \[mvr=\frac{nh}{2\pi }\]                               ?. (i) Also, the electrostatic force of attraction between the nucleus and electron is equal to centripetal force.                 \[\frac{m{{v}^{2}}}{r}=\frac{1}{4\pi {{\varepsilon }_{0}}}\frac{Ze\times e}{{{r}^{2}}}\]     ? (ii)      From Eqs. (i) and (ii), we get                 \[{{r}_{n}}={{n}^{2}}\frac{{{h}^{2}}{{\varepsilon }_{0}}}{\pi mZ{{e}^{2}}}\] \[\Rightarrow \]               \[{{r}_{n}}\propto \frac{{{n}^{2}}}{Z}\]