Scientists are now beginning to study "large" atoms, that...

Scientists are now beginning to study "large" atoms, that is, atoms with orbits that are almost large enough to be measured in our everyday units of measurement. For what excited state (give an approximate principal quantum number) of a hydrogen atom would the diameter of the orbit be in the order of $\left(10^{-5} \mathrm{~m}\right)$ - that is, close to the diameter of a human hair?

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Key Concepts

Atomic Orbit Scaling

Atomic orbit scaling refers to the relationship between the size of an atomic orbital and the quantum state of the electron. In the Bohr model, the radius of an orbit is proportional to the square of the principal quantum number, which allows for estimations of atomic sizes even when they reach scales that can be compared to everyday units of length, such as the diameter of a human hair.

Bohr Model

The Bohr model of the hydrogen atom describes electrons as moving in circular orbits around the nucleus with quantized angular momentum. This model introduces the concept of quantized orbital radii, where each orbit is associated with a particular energy level and radius that increases as the square of the principal quantum number.

Principal Quantum Number

The principal quantum number, denoted as n, specifies the energy level and size of the electron’s orbit around the nucleus in an atom. As n increases, the radius of the corresponding orbit grows approximately proportional to n squared, meaning that higher excited states have significantly larger orbital radii.

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