Atoms & Nuclei

JEE Main level, single correct, medium

92 of 239

Question 92 of 239

Suppose an electron is attracted towards the origin by a force k/rk / r where ' kk ' is a constant and ' rr ' is the distance of the electron from the origin. By applying Bohr model to this system, the radius of the nth n^{\text {th }} orbital of the electron is found to be ' rnr_n ' and the kinetic energy of the electron to be TnT_n. Then which of the following is true?

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Answer: (B) TnT_n independent of n,rn∝nn, r_n \propto n

kr=mv2rmv=k (independent or r ) n(h2π)=mvr⇒r∝n and T=12mv2 is independent of n.\begin{aligned} & \frac{\mathrm{k}}{\mathrm{r}}=\frac{m v^2}{\mathrm{r}} \\ & \mathrm{mv}=\mathrm{k} \quad \text { (independent or } r \text { ) } \\ & \mathrm{n}\left(\frac{\mathrm{h}}{2 \pi}\right)=m v r \Rightarrow r \propto \mathrm{n} \text { and } \mathrm{T}=\frac{1}{2} m v^2 \text { is independent of } \mathrm{n} . \end{aligned}

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