The radius of innermost orbit of hydrogen atom is . What is the radius of third allowed orbit of hydrogen atom? [2023]

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Solution

Q.
The radius of innermost orbit of hydrogen atom is $5.3 \times 10^{- 11} m$ . What is the radius of third allowed orbit of hydrogen atom [2023]

1 1.59 $Å$

2 4.77 $Å$

3 0.53 $Å$

4 1.06 $Å$

Ans.
(2)

Given, $r_{1} = 5.3 \times 10^{- 11} m$

Radius of $n^{th}$ orbit of Hydrogen atom is, $r_{n} = 0.53 \times \frac{n^{2}}{Z}$ $Å$

The radius of the third allowed orbit of hydrogen atom is, $r_{3} = 0.53 \times \frac{{(3)}^{2}}{1} Å$

$r_{3} = 47.7 \times 10^{- 11} m; r_{3} = 4.77 \times 10^{- 10} m or 4.77$ $Å$

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