Question

Derive the Bohr’s quantisation condition for angular momentum of the orbiting of electron in hydrogen atom, using de Broglie’s hypothesis.

Answer 1

Bohr's quantisation condition is $\text{L} = \frac{\text{n \ h}}{2\pi }$

Explanation:

The correct question is,

Obtains Bohr's quantisation condition for angular momentum of electron orbiting in nth hydrogen atom on the basis of the wave picture of an electron using de Broglie hypothesis.

Relation for wavelength by  De-brogile can be written as,

$\lambda = \frac{\text{h}}{\text{mv}} \ -----> (1)$

circumference of the and the standing wave condition is equal to the = whole Number of wave length.

$2\pi \text{r} = \text{n}\lambda\text{n} \ ----> (2)$

The angular momentum can written as,

L = mvr

From equation (1), the above relation can be written as

$\text{L} = \frac{\text{h r}}{\lambda}$

From equation (2), the above relation can be written as

$\text{L} = \frac{\text{h r}}{\frac{2\pi\text{r}}{n} }$

Bohr's Quantisation condition for angular momentum of electron orbiting in nth  hydrogen atom on the basis of the wave picture of an electron using de Broglie hypothesis can be written as,

$\text{L} = \frac{\text{n \ h}}{2\pi }$

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