The radius of the innermost electron orbit of a hydrogen atom is5.3×10–11 m. The radius of the n =3 orbit is
Question
The radius of the innermost electron orbit of a hydrogen atom is5.3×10–11 m. The radius of the n =3 orbit is
Solution
The radius of an electron orbit in a hydrogen atom is given by the formula:
r = n² * r₀
where:
- r is the radius of the orbit,
- n is the principal quantum number (the number of the orbit, starting from 1),
- r₀ is the radius of the innermost orbit (the first orbit, also known as the Bohr radius).
In this case, you are given that r₀ = 5.3×10⁻¹¹ m and you are asked to find the radius of the n = 3 orbit.
Substitute the given values into the formula:
r = 3² * 5.3×10⁻¹¹ m r = 9 * 5.3×10⁻¹¹ m r = 47.7×10⁻¹¹ m
So, the radius of the n = 3 orbit is 47.7×10⁻¹¹ m.
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