First slide

Bohr Model of the Hydrogen atom.

Question

If $ω_{0}$ be the orbital angular velocity of electron in the ground state of hydrogen atom, then which of the following may be the angular velocity of electron in any orbit in Li⁺⁺ ion?

Moderate

A

$ω_{0} / 0.25$
B

$ω_{0} / 4$
C

$ω_{0} / 2$
D

$ω_{0} / 6.75$

Solution

In the nth orbit of a He⁺ ion,
$ω_{n} = \frac{V_{n}}{r_{m}} = \frac{V_{0} \frac{z}{n}}{r_{0} \frac{n^{2}}{z}} = ω_{0} \frac{z^{2}}{n^{3}}$
For Helium, z = 2
For $n = 1, ω_{1} = ω_{0} \frac{2^{2}}{1^{3}} = 4 ω_{0}, for n = 2, ω_{2} = ω_{0} \frac{2^{2}}{2^{3}} = \frac{ω_{0}}{2}$
for $n = 3, ω_{3} = ω_{0} \frac{2^{2}}{3^{3}} = \frac{4 ω_{0}}{27} = \frac{ω_{0}}{6 .75}$

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