Question

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

• A. Relative change in the radii of two consequtive orbitals does not depend on Z.
• B. Relative change in the radii of two consequtive orbitals varies as 1/n.
• C. Relative change in the energy of two consequtive orbitals varies as $1/n^3$
• D. Relative change in the angular momenta of two consequtive orbitals varies as 1/n.

Answer 1

Answer: (A), (B), (D)

Relative change in the radii of two consequtive orbitals does not depend on Z.
Relative change in the radii of two consequtive orbitals varies as 1/n.
Relative change in the angular momenta of two consequtive orbitals varies as 1/n.

$r=r_0\left(\frac{n^2}{z}\right)$

$\frac{\Delta r}{r}=2\frac{\Delta n}{n}$

Since $\Delta n=1$,

$\frac{\Delta r}{r}\alpha \frac{1}{n}$

$L=\frac{nh}{2\pi }$

$\frac{\Delta L}{L}=\frac{\Delta n}{n}$

$\frac{\Delta L}{L}\alpha \frac{1}{n}$

Answer is ABD.