Question

Calculate the velocity of an electron placed in the second orbit of $L{i}^{2+}$ ion

<!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> AIIMS 2018

• A. $4.23\times {10}^{6}m.s^{-1}$
• B. $3.27\times {10}^{6}m.s^{-1}$
• C. $3.27\times {10}^{6}cm.s^{-1}$
• D. $0.521m.s^{-1}$

Answer 1

The correct option is B $3.27\times {10}^{6}m.s^{-1}$

The velocity of an electron in nth shell of the hydrogen like atom:
$=\frac{2.18\times {10}^6\times Z}{n}m.s^{-1}$
For $L{i}^{2+}:Z=3$
$n=2$ for second orbit:
$v=\frac{2.18\times {10}^6\times 3}{2}m.s^{-1}v=3.27\times {10}^{6}m.s^{-1}$