Q34 / 180 · AIIMS 2018 (26 May) · Chemistry

Calculate the velocity of an electron placed in the second orbit of $\mathrm{Li}^{2+}$ ion.

  • A
    $0.521 \mathrm{~m} \mathrm{~s}^{-1}$
  • B
    $3.27 \times 10^6 \mathrm{~cm} \mathrm{~s}^{-1}$
  • C
    $4.23 \times 10^3 \mathrm{~m} \mathrm{~s}^{-1}$
  • Correct answer
    D
    $3.27 \times 10^6 \mathrm{~m} \mathrm{~s}^{-1}$

Solution

The velocity of an electron in $n^{\text {th }}$ shell of the hydrogen like atom $=\frac{2.18 \times 10^6 \mathrm{~ms}^{-1} \times Z}{n}$ On putting $Z=3$ and $n=2$, $v=\frac{2.18 \times 10^6 \times 3}{2}=3.27 \times 10^6 \mathrm{~m} \mathrm{~s}^{-1}$

Hence, the correct answer is option: 'D'.

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