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

2 Answers

3 votes
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!
User Vopilif
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2 votes

Answer:


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

User Sharath Kumar
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