Question

The set of quantum numbers 'n' and 'l' possible for orbital shown in radial probability curve

Answer 1

Answer:

In an atom, the electronic space is divided into shells. Each shell is represented by a value of the principal quantum number n. For example, n = 1 is the lowest energy shell, called K shell, n = 2 is the second shell, L shell, and so on.

Atomic shells

Atomic shells

Within every shell, there are subshells. The number of subshells in a shell is decided by the azimuthal quantum number l. For every value of n, the possible values of l are 0, 1, 2 … n − 2, n − 1. Thus for K shell (n = 1), l = 0, for L shell (n = 2), l = 0, 1; for M shell (n = 3), l = 0, 1, 2, and so forth. Each value of l corresponds to a subshell. l = 0 is an s subshell, l = 1 is a p subshell, l = 2 is a d subshell, l = 3 is an f subshell etc. The table below summarizes the same.

Explanation:

Answer 2

To find:

The set of quantum numbers "n" and "l" possible for the orbital shown in the radial probability curve.

(Options given in image)

Diagram:

$\boxed{\setlength{\unitlength}{1cm}\begin{picture}(7,8)\put(1,1){\vector(1,0){5}}\put(1,1){\vector(0,1){5}}\qbezier{(1,1)(1.5,2)(3,1)}\qbezier{(3,1)(3.5,4)(4,1)}\put(0.5,3){D}\put(3,0.5){ {A}^{\circ} }\put(2,3){ \rm{\underline{2s\:orbital}} }\end{picture}}$

Calculation:

In the radial probability curve , we can see that the curve is touching the x axis for 1 time after origin.

Hence , the number of radial nodes = 1

So , it is possible in case of 2s orbital.

The Principal Quantum Number for this orbital is:

$\boxed{ \sf{PQN = n = 2}}$

The Azimuthal Quantum Number for this orbital is:

$\boxed{ \sf{AZN = l = 0}}$

So, the final answer is:

$\boxed{ \boxed{ \red{ \sf{n = 2 \: , \: l = 0}}}}$