JEE Advanced2016PhysicsAtomic PhysicsActual
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?
Options
- ARelative change in the radii of two consecutive orbitals does not depend on Z
- BRelative change in the radii of two consecutive oribitals varies as 1/n
- CRelative change in the energy of two consecutive orbitals varies as 1/ n 3
- DRelative change in the angular momenta of two consecutive orbitals varies as 1/n
Correct answer
A. Relative change in the radii of two consecutive orbitals does not depend on Z
Step-by-step solution
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