Question Bank › Physical Chemistry › Atomic Structure › ABC26PH0331ABC26PH0331 · Atomic Structure Subject: Physical Chemistry · Chapter: Atomic Structure · Topic: Atomic Structure – General · Exam: GATE 2005-2021 · Marks: 2 · Difficulty: Medium
The hydrogen-like radial wave function of the 3s orbital is given as \[ \mathrm{R}_{3,0}=\frac{1}{9\sqrt{3}}\left(\frac{\mathrm{Z}}{\mathrm{a}_{0}}\right)^{3/2}\left(6-2\rho+\frac{\rho^{2}}{9}\right) \mathrm{e}^{-\rho/6} \]
where $\rho=2\mathrm{Zr}/\mathrm{a}_{0}$; Z = atomic number; r = distance from the nucleus and $\mathrm{a}_{0}$ = Bohr radius. Positions of the radial nodes (in units of $\mathrm{a}_{0}$) of the 3s orbital are at (a) $\frac{3+3 \sqrt{3}}{2 Z}, \frac{3-3 \sqrt{3}}{2 Z}$
(b) $\frac{9+3 \sqrt{3}}{2 Z}, \frac{9-3 \sqrt{3}}{2 Z}$
(c) $\dfrac{3+\sqrt{3}}{2\mathrm{Z}}, \dfrac{3-\sqrt{3}}{2\mathrm{Z}}$
(d) $\dfrac{6+3\sqrt{3}}{2\mathrm{Z}}, \dfrac{6-3\sqrt{3}}{2\mathrm{Z}}$
Answer SELF-PRACTICE — the source book printed no answer.
Nothing is invented here, so this question has no answer on record.
Explanation No explanation was printed for this question.
← Previous in chapter · Chapter list · Next in chapter → Open in whiteboard · Browse this chapter in the app