Question

Ratio of radii of orbits corresponding to the first excited state and ground state in a hydrogen atom

Answer 1

Radius of the nth orbit   rn ∝ n2. 
For ground state n = 1 and for the first excited state n = 2.

Therefore   r2/r1 = 22/1 = 4/1 = 4:1.
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Answer 2

The the ratio of radii of orbits corresponding to the first excited state and ground state in a hydrogen atom  is 4 : 1.

Explanation:

To find, the the ratio of radii of orbits corresponding to the first excited state and ground state in a hydrogen atom  = ?

We know that,

The radius of the nth orbit  $r_{n}$ ∝ $n^2$

For ground state n = 1,

The radius of the ground state,

$r_{1} \alpha 1^2$

For first excited state n = 2,

The radius of the ground state,

$r_{2} \alpha 2^2$

∴ The the ratio of radii of orbits corresponding to the first excited state and ground state in a hydrogen atom  

$=\dfrac{r_{2}}{r_{1}}=\dfrac{4}{1}=4:1$

Hence, the the ratio of radii of orbits corresponding to the first excited state and ground state in a hydrogen atom  is 4 : 1.