Question

Compare the velocities of electron in
1. H 1st orbit
2. $H{e}^{+}$ 1st orbit
3. $L{i}^{++}$ 2nd orbit

• A. (1) > (2) > (3)
• B. (1) = (3) > (2)
• C. (1) < (3) < (2)
• D. None of these

Answer 1

The correct option is C (1) < (3) < (2)

$v_n=\frac{Z}{n}{V}_o$
Velocity of electron in the nth orbit for a Hydrogen like atom is given by the above formula. Here $v_o=2.19\times {10}^{6}m/s$
very close to the speed of light $\frac{1^{th}}{100}$ of 'c' but yet very close.
Let’s find for given cases
(1) H $1^{st}$ orbit
$Z_n=1$
n=1
$V=V_o$

(2) $H{e}^{+}{1}^{st}$ orbit
$Z_{He}=2$
n=1
$V=2V_o$

(3) $L{i}^{++}{2}^{nd}$ orbit
$Z_{Li}=3$
n=2
$V=\frac{3}{2}{V}_o$

(1) < (3) < (2)