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Characteristics of Bohr's Atomic Model

In Bohr's mod...

Question

In Bohr's model of hydrogen atom, radius of the first orbit of an electron is $r_{0}$ . Then, radius of the third orbit is?

A

\frac{r_{0}}{9}

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B

r_{0}

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C

3 r_{0}

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D

9 r_{0}

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Solution

The correct option is C $9 r_{0}$
Radius of the nth orbit of an electron is given by $r_{n} = r_{o} \frac{n^{2}}{Z}$
For hydrogen atom, $Z = 1$
$⟹ r_{n} = r_{o} n^{2}$
So, for third orbit $n = 3$
Thus radius of third orbit $r_{3} = r_{o} \times 3^{2} = 9 r_{o}$

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