First slide

Hydrogen -like ion

Question

If speed of electron in the ground state of hydrogen atom is $2.2 \times 10^{6} m / s$ , which of the following cannot be the speed of electron in any orbit of He⁺ ion?

Moderate

A

${2.2×10}^{6} m/s$
B

${1.466×10}^{6} m/s$
C

${4.4×10}^{6} m/s$
D

${3.46×10}^{6} m/s$

Solution

$V_{n} {=V}_{0} \frac{z}{n}$
In case of He⁺ ion, z = 2
$∴$ For $n = 1, V_{1} = 2 .2 \times 10^{6} \times \frac{2}{1} m / s = 4 .4 \times 10^{6} m / s$
For $n = 2, V_{2} = 2 .2 \times \frac{2}{2} \times 10^{6} m / s = 2 .2 \times 10^{6} m / s$
For $n = 3, V_{3} = 2 .2 \times \frac{2}{3} \times 10^{6} m / s = 1 .466 \times 10^{6} m / s$

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