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The ratio of the areas of the electron orbits for the first excited state and the ground state of the hydrogen atom is _______.

Asked in GUJCET 2009 · Postulates, radius, speed and angular momentum

Answer: (1) 16:1

Step-by-step solution

Idea: the orbit area is A=π r², and in the Bohr model r∝ n², so A∝ n⁴.

First excited state: n=2; ground state: n=1.

(r₂)/(r₁)=(2²)/(1²)=4.

(A₂)/(A₁)=((r₂)/(r₁))²=4²=16.

So the ratio is 16:1.

Why the other options are wrong

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