Question

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

• A. $8 : 3$
• B. $3 : 2$
• C. $3 : 8$
• D. $2 : 3$

Answer 1

Answer: (D)

$\frac{\Delta R_{1}}{\Delta R_{2}}=\frac{\left(r_{4}-r_{3}\right)_{4^{2+}}}{\left(r_{4}-r_{3}\right)_{H e^{+}}}$

$=\frac{\frac{4^{2}}{3}-\frac{3^{2}}{3}}{\frac{4^{2}}{2}-\frac{3^{2}}{2}}$

$=\frac{7 / 3}{7 / 2}=\frac{2}{3}$