First slide

Hydrogen -like ion

Question

Consider 3^rd orbit of He⁺ (Helium) Using non relativistic approach, the speed of electron in this orbit will be (given K = 9 × 10⁹ constant, Z = 2 and h= 6.6×10^-34 Js) (Plancks constant=h)

Difficult

A

0.73 × 10⁶m/s
B

3.0 × 10⁸ m/s
C

2.92 × 10⁶ m/s
D

1.46 × 10⁶ m/s

Solution

We know that velocity $V = \frac{e^{2}}{4 πKh} \frac{2}{n}$
$= \frac{{(1.6 x 10^{- 19})}^{2}}{4 x \frac{22}{7} x 9 x 10^{9} x 6.6 x 10^{- 34}} x \frac{2}{3} = 1.46 x 10^{6}; (shortcut) V = \frac{c}{137} \frac{z}{n} = \frac{3 x 10^{8}}{137} x \frac{2}{3} = \frac{2}{137} x 10^{8} = 1.46 x 10^{6}$

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