What is the relations between radius, of order orbit and nuclear charge for hydrogen like species?

What is the relations between radius, of order orbit and nuclear charge for hydrogen like species?
  1. $r_n=\frac{a_0 n^2}{z} p m$
  2. $r_n=\frac{a_0 n^2}{z^2} p m$
  3. $r_n=\frac{a_0 n}{n^2} p m$
  4. $r_n=\frac{a_0 z}{n^2} p m$

Solution

Radius of nth orbit of an atom is $\mathrm{R}_{\mathrm{n}}=0.529 \frac{\mathrm{n}^2}{\mathrm{z}} Å$ $r_1$ of Hydrogen atom $=0.529 Å=a_0$ $\therefore \mathrm{r}_{\mathrm{n}}=\mathrm{a}_0 \frac{\mathrm{n}^2}{\mathrm{z}}$

Asked in: MHT CET 2022 (11 Aug Shift 1)

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