Highly excited states for hydrogen like atoms (also called Rydberg states) with nuclear charge Ze are defined by their principal quantum number n, where n 1. Which of the following statement(s) is

Question

Highly excited states for hydrogen like atoms (also called Rydberg states) with nuclear charge Ze are defined by their principal quantum number n, where n >> 1. Which of the following statement(s) is (are) true?

TestHub · Accepted Answer

As radius r ∝ n 2 z 0 ⇒ ∆ r r = n + 1 z 2 - n z 2 n z 2 = 2 n + 1 n 2 ≈ 2 n ∝ 1 n As energy E ∝ z 2 n 2 ⇒ ∆ E E = z 2 n 2 - z 2 n + 1 2 z 2 n + 1 2 = n + 1 2 - n 2 n 2 . n + 1 2 . n + 1 2 ⇒ ∆ E E = 2 n + 1 n 2 ≃ 2 n n 2 ∝ 1 n As angular momentum L = n h 2 π ⇒ ∆ L L = n + 1 h 2 π - n h 2 π n h 2 π = 1 n ∝ 1 n

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