Question

Which of the following combinations of statements is true regarding the interpretation of the atomic orbitals?
a.An electron is an orbital of high angular momentum stays away from the nucleus than an electron in the orbital of lower angular momentum.
b.For a given value of the principal quantum number, the size of the orbital is inversely proportional to the azimuthal quantum number.
c.According to wave mechanics, the ground state angular momentum is ${\displaystyle \frac{\text{h}}{2\pi }}$
d.The plot of $\mathrm{\Psi }$ vs r for various azimuthal quantum numbers, show peak shifting towards a higher value.
A.b, c
B.a, d
C.a, b
D.a, c

Answer 1

Hint: A thorough knowledge on atomic structure is necessary to answer this question. The angular momentum of the electron has the following formula: $\text{mvr = n}{\displaystyle \frac{\text{h}}{2\pi }}$ where, ‘n’ is the principal quantum number of the orbital.

Complete step by step answer:
Coming to the first point, from the equation of the angular momentum, it is clear that the angular momentum is directly proportional to the principal quantum number of an electron, ${\displaystyle \frac{\text{h}}{2\pi }}$ being a constant. So, as the principal quantum number increases, the distance of the electron from the nucleus also increases.
Hence, as any electron moves away from the nucleus, its angular momentum also increases. So, this option is correct.
In the second point, it is said that for any principal quantum number, the size of the orbital is inversely proportional to the azimuthal quantum number which is wrong because the principal quantum number is independent of the azimuthal quantum number. So, this option is also incorrect.
The third point says that According to wave mechanics, the ground state angular momentum is ${\displaystyle \frac{\text{h}}{2\pi }}$ which is true because the angular momentum $\text{mvr = n}{\displaystyle \frac{\text{h}}{2\pi }}$ putting n = 1, which is the least value of n, we get that $\text{mvr = }{\displaystyle \frac{\text{h}}{2\pi }}$ . So, this option is correct.
Coming to the last point, the plot of $\mathrm{\Psi }$ vs r for various azimuthal quantum numbers, where $\mathrm{\Psi }$ is the wave function or atomic orbitals or the probability of finding an electron, and the value of the peak of the plot of $\psi$ vs r for various azimuthal quantum numbers increases in all directions, with the value of n, or the principal quantum number. So, this option is also incorrect.

Hence, the correct option is only statement (a) and (c), i.e. option (D).

Note:
-The principal quantum number ‘n’ denotes the shell number of the electron.
-The azimuthal quantum number ‘l’ denotes the subshell number of the electron.
-The magnetic quantum number ‘m’ denotes the orbital number of the electron.
-The spin quantum number ‘s’ denotes the spin value or the direction of rotation of the electron.
- According to Pauli’s Exclusion principle, “no two electrons can have the same set of all four quantum numbers”. So, two electrons in the same orbital will have opposite spins to balance each other.