First slide

Hydrogen -like ion

Question

How many times larger is the spacing between the energy levels with n = 3 and n = 4, than the spacing between the energy levels with n = 8 and n = 9 for a hydrogen like atom or ion?

Moderate

Solution

Radius of hydrogen atom in $n^{th}$ energy state is, $r_{n} = r_{o} . n^{2}$
The required ratio = $\frac{r_{4} - r_{3}}{r_{9} - r_{8}} = \frac{4^{2} - 3^{2}}{9^{2} - 8^{2}} = \frac{7}{17} = 0 .411.$

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