Question

Determine the linear momentum of the electron in the second Bohr orbit of a hydrogen atom. Hence determine the linear momentum in the third Bohr orbit.​

Answer 1

Given,

Two Bohr orbits (n = 2 and 3)

To find,

The linear momentum of the electron at the Bohr orbit n = 2 and 3.

Solution,

The linear momentum in the second Bohr orbit of a hydrogen atom is x and the linear momentum in the third Bohr orbit of a hydrogen atom is 1.5x if x = $\frac{h}{pie}$.

We can simply solve this numerical problem by the following method.

We know that,

Angular momentum (or moment of linear momentum) of an electron in the nth orbit of Bohr's hydrogen atom is given by :

Linear momentum = $\frac{nh}{2(pie)}$,

where,

n = the number of Bohr orbit

h = Planck's constant

Now,

It is given that n = 2 and n = 3.

Thus,

Linear momentum at (n = 2) = $\frac{2h}{2*3.14}$

                                              = $\frac{h}{pie}$

Linear momentum at (n=3) = $\frac{3h}{2(pie)}$

As a result, the linear momentum in the second Bohr orbit of a hydrogen atom is x and the linear momentum in the third Bohr orbit of a hydrogen atom is 1.5x if x = $\frac{h}{pie}$.