MCQ
The difference between the radii of $3^{\text {rd }}$ and $4^{\text {th }}$ orbits of $Li ^{2+}$ is $\Delta R _{1}$. The difference between the radii of $3^{\text {rd }}$ and $4^{\text {th }}$ orbits of $He ^{+}$ is $\Delta R _{2}$. Ratio $\Delta R _{1}: \Delta R _{2}$ is :
  • A
    $8:3$
  • B
    $3:2$
  • C
    $3:8$
  • $2:3$

Answer

Correct option: D.
$2:3$
d
$\frac{\Delta R _{1}}{\Delta R _{2}}=\frac{\left( r _{4}- r _{3}\right)_{4^{2+}}}{\left( r _{4}- r _{3}\right)_{ He ^{+}}}=\frac{\frac{4^{2}}{3}-\frac{3^{2}}{3}}{\frac{4^{2}}{2}-\frac{3^{2}}{2}}=\frac{7 / 3}{7 / 2}=\frac{2}{3}$

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