(a) What is the difference in radius between the n=1 state...

(a) What is the difference in radius between the $n=1$ state and the $n=2$ state for hydrogen? (b) What is the difference in radius between the $n=100$ state and the $n=101$ state for hydrogen? How do the neighboring orbital separations compare for large and small $n$ values?

Labs

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

Key Concepts

Bohr Model for the Hydrogen Atom

The Bohr model describes the hydrogen atom with quantized, circular electron orbits. It introduces the idea that electrons exist in discrete orbits whose radii are determined by the principal quantum number n. Specifically, the radius of the nth orbit is given by r? = a?·n², where a? is the Bohr radius. This model provides a simple formula to compute differences in radii between different energy levels.

Dependence of Orbital Radius on Quantum Number

Because the orbital radius in the hydrogen atom scales as the square of the principal quantum number (n²), the spacing between successive orbits is not uniform. For example, the difference in radii between low-lying states (such as n = 1 and n = 2) is relatively small in absolute terms, while for high n values the absolute change (given by (2n + 1)a?) becomes large. However, the fractional change relative to the orbital size becomes smaller as n increases, meaning that neighboring orbitals for large n values are closer together relative to the size of the orbit compared to those at small n.

Transcript

Please give Ace some feedback