Question

Assertion: There are two spherical nodes in the $3s$ orbital.
Reason: There is no planar node in the $3s$ orbital.
A.Both assertion and reason are correct and the reason is the correct explanation for the Assertion.
B.Both assertion and reason are correct but the reason is not the correct explanation for the Assertion.
C.Assertion is correct but the reason is incorrect.
D.Both Assertion and Reason are incorrect.

Answer 1

The nodes in a molecular or an atomic orbital are defined as the areas where the probability of finding the electron is zero. It can be calculated from the formula.

Formula used:
$r = n - l - 1$
Where r is the number of nodes, n is the principal quantum number and l is the azimuthal quantum number.

Complete step by step solution:
In terms of quantum mechanics, the node is defined as the place where the quantum mechanical wave function $\Psi$ and its square ${\Psi ^2}$ change their phase.
There are different types of nodes, the radial nodes in an orbital is given by the formula,
$r = n - l - 1$
For the $3s$, the principal quantum number = 3 and the azimuthal quantum number = 0.
Hence, the value of the number of radial/ spherical nodes = $3 - 0 - 1 = 2$ , while the number of angular/ planer nodes = 0.
So, both the assertion and the reason are correct but the reason is not the correct explanation for the assertion.

Hence, the correct answer is option B.

Note: Radial or spherical nodes are is the spherical surface on an atom, where the probability of finding the electron is zero while the angular node or the planar node is the plane that passes through the nucleus where the probability of finding the electron is zero.