The difference between the radii of 3 ^ rd and 4 ^ th orbits of L _...

$r = 0 . 529\dfrac{{n}^{2}}{7}A$

For ${Li}^{2 +}$

${\left(r{L}^{2 +}\right)}_{n = 4} - {\left(r{L}^{2 +}\right)}_{n = 3} = \dfrac{0 . 529}{3} [ 16 - 9 ] = \Delta{R}_{1}$

For ${He}^{+}$

${\left(r{He}^{+}\right)}_{n = 4} - {\left(r{He}^{+}\right)}_{n = 3} = \dfrac{0 . 529}{2} [ 16 - 9 ] = \Delta{R}_{2}$

$\dfrac{{\Delta R}_{1}}{{\Delta R}_{2}} = \dfrac{2}{3}$