Q137 / 180 · KCET 2022 · Physics

If an electron is revolving in its Bohr orbit having Bohr radius of $0.529 Å$, then the radius of third orbit is

  • A
    $4496 Å$
  • Correct answer
    B
    $4.761 Å$
  • C
    $5125 \mathrm{~nm}$
  • D
    $4234 \mathrm{~nm}$

Solution

Given, Bohr radius, $r_1=0.529 Å$ We know that, radius of revolving electron in $n$th orbit is given as $$ r \propto n^2 $$ $$ \begin{array}{ll} \Rightarrow & r_1=\left(\begin{array}{l} n_1 \\ n_2 \end{array}\right)^2 \\ \Rightarrow & \frac{r_1}{r_2}=\left(\frac{1}{3}\right)^2=\frac{1}{9} \quad\left[\because n_1=1 \text { and } n_2=3\right] \\ \Rightarrow & r_2=9 r_1=9 \times 0.529=4.761 Å \end{array} $$

Hence, the correct answer is option: 'B'.

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