(B) According to Bohr's theory,the velocity of an electron in the $n^{th}$ orbit of a hydrogen-like atom is given by the formula:$v_n = v_0 \times \fr

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(B) According to Bohr's theory,the velocity of an electron in the $n^{th}$ orbit of a hydrogen-like atom is given by the formula:$v_n = v_0 \times \frac{Z}{n}$where $v_0 = 2.18 \times 10^6 \; m/s$ is the velocity of an electron in the first orbit of the hydrogen atom.For $He^{+}$,$Z = 2$ and for the $3^{rd}$ orbit,$n = 3$.Substituting these values:$v_3 = (2.18 \times 10^6) \times \frac{2}{3} \; m/s$$v_3 = 2.18 \times 10^6 \times 0.666... \; m/s$$v_3 \approx 1.453 \times 10^6 \; m/s \approx 1.46 \times 10^6 \; m/s$.

Class 12 Physics Atoms Bohr's Model of Hydrogen Atom

Medium

Consider the $3^{rd}$ orbit of $He^{+}$ (Helium) using a non-relativistic approach. The speed of the electron in this orbit will be (given $K = 9 \times 10^9 \; N \cdot m^2/C^2$,$Z = 2$,and $h = 6.6 \times 10^{-34} \; J \cdot s$).

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A
$2.92 \times 10^6 \; m/s$
B
$1.46 \times 10^6 \; m/s$
C
$0.73 \times 10^6 \; m/s$
D
$3.0 \times 10^8 \; m/s$

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Bohr's Model of Hydrogen Atom

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Consider the $3^{rd}$ orbit of $He^{+}$ (Helium) using a non-relativistic approach. The speed of the electron in this orbit will be (given $K = 9 \times 10^9 \; N \cdot m^2/C^2$,$Z = 2$,and $h = 6.6 \times 10^{-34} \; J \cdot s$).

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