As the principal quantum number n increases, which statement is true?

As the principal quantum number n increases, which statement is true?

• A. The distance from the nucleus decreases
• B. The energy remains constant
• C. The distance from the nucleus increases
• D. The electrons contract toward the nucleus as n increases

Answer: (C)

The principal quantum number n determines the size of an orbital and how tightly the electron is bound. As n increases, the orbital becomes larger, and the electron's average distance from the nucleus grows. In hydrogen-like systems, the radius scales roughly with n^2, and the energy becomes less negative as n increases (the electron is less tightly bound). So the distance from the nucleus increases with increasing n. The other statements conflict with how higher-n orbitals behave: they do not contract or stay at the same distance or energy as n grows.

The principal quantum number n determines the size of an orbital and how tightly the electron is bound. As n increases, the orbital becomes larger, and the electron's average distance from the nucleus grows. In hydrogen-like systems, the radius scales roughly with n^2, and the energy becomes less negative as n increases (the electron is less tightly bound).

So the distance from the nucleus increases with increasing n. The other statements conflict with how higher-n orbitals behave: they do not contract or stay at the same distance or energy as n grows.