Question

calculate the diameter of the fifteen orbit of the hydrogen atom if the diameter of the innermost orbit is 1.06 A

Answer 1

We know, dₓ α n² d₁

For n = 15 (15th Orbit)

It would be: d₁₅ = 15² * 1.06

d₁₅ = 238.5 A

In short, Your Answer would be: 238.5 A

Hope this helps!

Answer 2

`r_(n) =n^(2) *r_(1)=15^(2) *0.53A=119.25A`

Step-by-step explanation:

Following the Bohr model radii, where
`r_(n) =n^(2) *r_(1)` for the hydrogen atom, we can calculate the nth radius if we know the first one, as long as n is a whole number.

The problem gives us the first diameter, and we also know that d=2r so
`r_(1)=(d_(1) )/(2)`

`r_(1)=(d_(1) )/(2)=(1.06 A)/(2) =0.53A`

Now we change this value in the Bohr model radii formula:

`r_(n) =n^(2) *r_(1)=15^(2) *0.53A=119.25A`