JEE Advanced 2016Paper 1
- Exam
- JEE Advanced
- Year
- 2016
- Paper
- Paper 1
- Subject
- Physics
- Chapter
- Atomic Physics
JEE Advanced 2016 · Paper 1 · Physics · Atomic Physics
Highly excited states for hydrogen like atoms (also called Rydberg...
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/
- 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
As energy
⇒ \dfrac{∆ E}{E} = \dfrac{\dfrac{{z}^{2}}{{n}^{2}} - \dfrac{{z}^{2}}{{\left(n + 1\right)}^{2}}}{\dfrac{{z}^{2}}{{\left(n + 1\right)}^{2}}} = \dfrac{{\left(n + 1\right)}^{2} - {n}^{2}}{{n}^{2} . {\left(n + 1\right)}^{2}} . {\left(n + 1\right)}^{2}
As angular momentum
As energy
⇒ \dfrac{∆ E}{E} = \dfrac{\dfrac{{z}^{2}}{{n}^{2}} - \dfrac{{z}^{2}}{{\left(n + 1\right)}^{2}}}{\dfrac{{z}^{2}}{{\left(n + 1\right)}^{2}}} = \dfrac{{\left(n + 1\right)}^{2} - {n}^{2}}{{n}^{2} . {\left(n + 1\right)}^{2}} . {\left(n + 1\right)}^{2}
As angular momentum