Question

Find the ratio of diameter of electron in 1st Bohr orbit to that in 4th bohr orbit.
(Ans : 1:16)

Answer 1

diameter = 1.06 n^2/Z ev

SO ratio = 1/4^2 =1/16

Answer 2

Answer:

1 : 16

Explanation:

Given Find the ratio of diameter of electron in 1st Bohr orbit to that in 4th bohr orbit.

Given r 1 be the radius of n th Bohr’s orbit. Now we need to find the diameter of nth Bohr’s orbit. So it will be D1 : D4

We know that r 1 = Ɛo h^2 n^2 / π m e^2

Now D n = 2  r 1

Let n = 1

D 1  = 2  Ɛo h^2 1^2 / π m e^2

D 1 = = 2 Ɛo h^2  / π m e^2

Now let n = 4

D  = = 2 Ɛo h^2 n^2 / π m e^2

D 4  =   2  Ɛo h^2 4^2 / π m e^2

 D 4 = = 2 Ɛo h^2  16 / π m e^2

So D 1 / D 4 = = 2 Ɛo h^2  / π m e^2 / 16 (2 Ɛo h^2  / π m e^2)

Now D 1 / D 4 = 1/16

So D1 : D4 = 1 : 16