Question

List – I	List - II
I) Radial probability distribution curve of $3s$ orbital	a) $1.1A$
II) Distance of maximum probability of $1s$ electron	b) $1s$ orbital
III) Radial node for a $2s$ electron	c) $3$ peaks, $2$ radial nodes
IV) No spherical nodes	d) $0.53A$

The correct match is:
A. I-a, II-b, III-c, IV-d
B. I-c, II-d, III-a, IV-b
C. I-b, II-a, III-d, IV-c
D. I-d, II-a, III-b, IV-c

Answer 1

Radial probability is defined as the probability of finding an electron at a distance between the radius and nucleus. The value of radial probability will always be small near the nucleus. The radial formula can be calculated by the product of radial probability density and volume.

Complete step-by-step answer:
Let us discuss the correct match from the given options.
I) The radial probability distribution curve of $1s$ orbital consists of one peak and zero radial node. The radial probability distribution curve of $2s$ orbital consists of two peaks and one radial node. The radial probability distribution curve of $3s$ orbital consists of three peaks and two radial nodes.
II) As we know that the probability of finding an electron at nucleus is zero, but as we increase the distance from the nucleus, the probability of finding an electron increases, so the probability of finding an electron at a maximum distance of $0.53{{A}^{{}^\circ }}$ . This is also known as Bohr’s first radius.
III) As we have discussed that the radial probability curve of $2s$ orbital contains two peaks and one radial node, radial node for $2s$ electron is at a distance of $1.1{{A}^{{}^\circ }}$ .
IV) $1s$ orbital contains zero nodes. Let us discuss how.
Number of nodes in $1s$ orbital is:
$n-1-l$
Where, $n=1$ and $l=0$ because of $s$ orbital.
Therefore, on substituting the value, we get,
$1-1-0=0$
Hence, we can say that there are no spherical nodes.
Therefore, the correct match is option (B) I-c, II-d, III-a, IV-b.

List – I	List - II
I) Radial probability distribution curve of $3s$ orbital	c) $3$ peaks, $2$ radial nodes
II) Distance of maximum probability of $1s$ electron	d) $0.53A$
III) Radial node for a $2s$electron	a) $1.1A$
IV) No spherical nodes	b) $1s$ orbital

Note: Node is defined as a point at which the probability of an electron is zero. Nodes are classified in two points.
Radial node: it is defined as a spherical surface where electron probability is zero. It is also known as nodal region. As we increase the quantum number, the number of radial nodes also increases.
Angular node: it is defined as a plane that passes through the nucleus. It is also known as nodal plane. The azimuthal quantum number is equal to the angular node.