First slide

Bohr Model of the Hydrogen atom.

Question

The radius of the Bohr orbit in the ground state of hydrogen atom is $0 .5 \overset{0}{A}$ . Then the radius of the orbit of the electron in the third excited state of ${He}^{+}$ ion is

Moderate

A

$2 \overset{0}{A}$
B

$4 \overset{0}{A}$
C

$6 \overset{0}{A}$
D

$8 \overset{0}{A}$

Solution

$\begin{array}{l} r_{n} = r_{0} . \frac{n^{2}}{Z}, where r_{0} = radius of bohr orbit \\ ∴ For {He}^{+} ion, r_{4} = 0 .5 \times \frac{4^{2}}{2} \overset{0}{A} = 4 \overset{0}{A} \end{array}$

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