The de-Broglie equation treats an electron to be

The wave function of $3\mathrm{s}$ electron is given by  ${\mathrm{\psi }}_{3\mathrm{s}}=\frac{1}{81\sqrt{3}\mathrm{\pi }}{\left(\frac{1}{{\mathrm{a}}_0}\right)}^{3/2}\left[27-18\left(\frac{\mathrm{r}}{{\mathrm{a}}_0}\right)+2{\left(\frac{\mathrm{r}}{{\mathrm{a}}_0}\right)}^2\right]{\mathrm{e}}^{-\mathrm{r}/3{\mathrm{a}}_0}$

It has a node at $\mathrm{r}={\mathrm{r}}_0$. Find the relations between ${\mathrm{r}}_0$ and ${\mathrm{a}}_0$.

A neutral atom has $2 \mathrm{K}$ electrons, $8 \mathrm{L}$ electrons and $6 \mathrm{M}$ electrons. Predict from this: its atomic number.

A neutral atom has $2\mathrm{K}$ electrons, $8\mathrm{L}$ electrons and $6\mathrm{M}$ electrons. From this, predict the total number of $\mathrm{s}$ electrons.

A neutral atom has $2 \mathrm{K}$ electrons, $8 \mathrm{L}$ electrons and $6 \mathrm{M}$ electrons. From this predict the total number of $\mathrm{p}$ electrons.

A neutral atom has $2 \mathrm{K}$ electrons, $8 \mathrm{L}$ electrons and $6 \mathrm{M}$ electrons. From this, predict the total number of $\mathrm{d}$ electrons.