Atomic Structure Result Question 9-1
9. Which of the following combination of statements is true regarding the interpretation of the atomic orbitals?
(2019 Main, 9 Jan II)
I. An electron in an orbital of high angular momentum stays away from the nucleus than an electron in the orbital of lower angular momentum.
II. For a given value of the principal quantum number, the size of the orbit is inversely proportional to the azimuthal quantum number.
III. According to wave mechanics, the ground state angular momentum is equal to $\dfrac{h}{2 \pi}$.
IV. The plot of $\psi$ vs $r$ for various azimuthal quantum numbers, shows peak shifting towards higher $r$ value.
(a) I, III
(b) II, III
(c) I, II
(d) I, IV
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Answer:
Correct Answer: 9. (d)
Solution:
- (I) Angular momentum, $m v r=\dfrac{n h}{2 \pi}$
$\Rightarrow \quad m v r \propto n$ $\propto$ distance from the nucleus
(II) This statement is incorrect as size of an orbit $\propto$ Azimuthal quantum number $(l)$
$(\because n=$ constant $)$
(III) This statement is incorrect as at ground state,
$n=1, l=0$
$\Rightarrow$ Orbital angular momentum (wave mechanics)
$=\sqrt{l(l+1)} \dfrac{h}{2 \pi}=0 \quad[\because l=0]$
(IV) The given plot is
BETA
