Assume that the radius of the first Bohr orbit of hydrogen atom is . The radius of the third Bohr orbit of is _______ picometer. (Nearest integer) [2023]

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Solution

Q.
Assume that the radius of the first Bohr orbit of hydrogen atom is $0.6 Å$ . The radius of the third Bohr orbit of ${He}^{+}$ is _______ picometer. (Nearest integer) [2023]

Ans.
(270)

$r_{n} = r_{0} \frac{n^{2}}{Z}$

${(r_{1})}_{H} = r_{0} \frac{{(1)}^{2}}{1} = 0.6 Å$

${(r_{3})}_{{He}^{+}} = r_{0} \frac{n^{2}}{Z}$

$= 0.6 \frac{(3^{2})}{2} = 0.6 \times \frac{9}{2} = 2.7 Å = 270 picometer.$

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