The radius of the innermost electron orbit of a hydrogen atom is 5.3×10–11 m. What are the radii of the n = 2 and n =3 orbits?

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The radius of the innermost electron orbit of a hydrogen atom is 5.3×10^–11 m. What are the radii of the n = 2 and n =3 orbits?

The radius of the innermost electron orbit of a hydrogen atom is 5.3×10^–11 m. What are the radii of the n = 2 and n =3 orbits?

Answer –

We are given the radius of the innermost orbit of a hydrogen atom as

r₁= 5.3 × 10⁻¹¹ m.

Suppose r₂represents the radius of the orbit for the level n = 2. Then, It will related to the radius of the inner most orbit as:

${{r}_{2}}={{n}^{2}}{{r}_{1}}=4\times 5.3\times {{10}^{-11}}m$

${{r}_{2}}=2.12\times {{10}^{-10}}m$

For n = 3, the corresponding electron radius is given by –

${{r}_{3}}=9\times 5.3\times {{10}^{-11}}=4.77\times {{10}^{-10}}m$

Therefore, the radii of an electron for n = 2 and n = 3 orbits are 2.12 × 10⁻¹⁰ m and 4.77 × 10⁻¹⁰ m respectively.

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