The radius of inner most orbit of hydrogen atom is 5 . 3 × 10 - 11 m . What is the radius of third allowed orbit of hydrogen atom?NEET 2023 (All India)

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TestHub · Accepted Answer

The formula to calculate the radius of the $n^{th}$ orbit is given by
$r_{n} = \frac{n^{2}}{Z} . . . (1)$
Substitute proper values of the orbit numbers in order to calculate the formula for the radius of the innermost and third allowed orbital radii.
$\begin{array}{rcl} r_{1} & = & \frac{1^{2}}{1} \\ = & 1 . . . (2) \\ r_{3} & = & \frac{3^{2}}{Z} \\ = & 9 . . . (3) \end{array}$
Divide equation (2) by equation (3) and solve to calculate the radius of the third allowed orbit.
$\begin{array}{rcl} \frac{r_{1}}{r_{3}} & = & \frac{1}{9} \\ r_{3} & = & 9 r_{1} \\ = & 9 \times 5.3 \times 10^{- 11} m \\ = & 47.7 \times 10^{- 11} m \\ = & 4.77 \overset{\circ}{A} \end{array}$

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