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

Answer:

$r_{n} =n^{2} *r_{1}=15^{2} *0.53A=119.25A$

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 $r_{1}=\frac{d_{1} }{2}$

$r_{1}=\frac{d_{1} }{2}=\frac{1.06 A}{2} =0.53A$

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

$r_{n} =n^{2} *r_{1}=15^{2} *0.53A=119.25A$