Chemistry - Atomic Structure Question with Solution | TestHub

For node${\mathrm{\psi }}^2=0$, So also$\mathrm{\Psi }=0$
So for:$\mathrm{\psi }=\frac{1}{16\sqrt{4}}{\left(\frac{1}{{\mathrm{a}}_{\mathrm{o}}}\right)}^{\frac{3}{2}}\left[\left(\mathrm{x}-1\right)\left({\mathrm{x}}^2-8\mathrm{x}+12\right)\right]{\mathrm{e}}^{-\frac{\mathrm{x}}{2}}$
$\left[\left(\mathrm{x}-1\right)\left({\mathrm{x}}^2-8\mathrm{x}+12\right)\right]$should be equal to zero
$\left[\left(\mathrm{x}-1\right)\left({\mathrm{x}}^2-8\mathrm{x}+12\right)\right]=0$, solve the equation
$\left(\mathrm{x}-1\right)\left({\mathrm{x}}^2-8\mathrm{x}+12\right)$
$\mathrm{X}=1,\mathrm{ }2,\mathrm{ }6$
$\mathrm{i}.\mathrm{e}.\mathrm{r}=0.5{\mathrm{a}}_{\mathrm{o}},{\mathrm{a}}_{\mathrm{o}},3{\mathrm{a}}_{\mathrm{o}};$
$\because \mathrm{x}=\frac{2\mathrm{r}}{{\mathrm{a}}_{\mathrm{o}}}$
So minimum$0.5{\mathrm{a}}_{\mathrm{o}}$
maximum$\mathrm{ }3{\mathrm{a}}_{\mathrm{o}}$