Question

What is the change in angular momentum,in hydrogen atom when electron jumps from the third orbit to the first orbit ?

Answer 1

Angular momentum of electron in third orbit of hydrogen atom is 3h/2pie which is equal to 1.5h/pie. Angular momentum was proposed by Neil Bohr. It gives the angular momentum of electron revolving in a circular orbit. Hence angular momentum of electron in third orbit the hydrogen is 1.5h/pie.

Answer 2

The change in angular momentum is $2.11 \times 10^{-34} \ \text{Js}$

Explanation:

Given Data

FInd the change in angular momentum in hydrogen atom when an electron jumps from the third to the first orbit.

The product of moment of inertia and angular velocity of the rotating object is called as Angular Momentum (L).

                                  L = m × v × r

                             $\text{m} \times \text{v} \times \text{r} = \frac{\text{n} \times \text{h}}{2 \pi}$

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

Where n is the orbit number

           h is the Planck's constant

For third orbit,

$\text{n} = 3 \ \text{and} \ \text{h} = 6.626176 \times 10^{34} \ \text{joule}-\text{seconds}.$

$\ \text{L} = \frac{3 \times \text{h}}{2 \pi} -------> (1)$

For first orbit, n = 1

$\ \text{L} = \frac{1 \times \text{h}}{2 \pi} -------> (2)$

Subtract (2) from (1)

$\text {Change in Angular Momentum } = \frac{3 \times \text{h}}{2 \pi} - \frac{ \text{h}}{2 \pi}$

$\text {Change in Angular Momentum } = \frac{\text{h}}{2 \pi} (3-1)$

$\text {Change in Angular Momentum } = \frac{2 \times \text{h}}{2 \pi}$

$\text {Change in Angular Momentum } = \frac{ \text{h}}{\pi}$

Substitute the respective values in above relation, where π = 3.14

$\text {Change in Angular Momentum } = \frac{ 6.626 \times 10^{34} \ }{3.14}$

$\text {Change in Angular Momentum } = 2.11 \times 10^{34} \ \text{Js}$

Therefore the change in angular momentum is $2.11 \times 10^{-34} \ \text{Js}$ when an electron from hydrogen atom jumps from the third orbit to the first orbit.

To Learn More

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