First slide

Bohr Model of the Hydrogen atom.

Question

If L be the orbital angular momentum of an hydrogen atom and r be radius of the atom then

Moderate

A

$L \propto r^{2}$
B

$L \propto \frac{1}{\sqrt{r}}$
C

$L \propto r$
D

$L \propto \sqrt{r}$

Solution

(4)
For an hydrogen atom,
$r = r_{0} n^{2} w h e r e r_{0} =$ radius of atom in ground state.
Again
$\begin{array}{l} L = n . \frac{h}{2 π} \\ ∴ r = r_{0} \times {(\frac{2 π L}{h})}^{2} \Rightarrow L^{2} = (\frac{h^{2}}{4 π^{2} r_{0}}) r \\ \Rightarrow L \propto \sqrt{r} \end{array}$

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