Question
The plot of radial probability density ($4\pi r^{2} R^{2}$) against $r$ for an electron in $np$ orbital of a many electron atom is given below. The value of $n$ is
This question was previously asked in
WBJEE 2026 Physics and Chemistry Question Paper (24-May-2026)
The correct answer is
3
To determine the value of \(n\) for the given radial probability density plot of the \(np\) orbital, we need to understand the characteristic features of these plots. The plot shows the behavior of \(4\pi r^{2} R^{2}\) (radial probability density) against the radial distance \(r\).
Radial Nodes:
- Radial nodes are regions where the probability density is zero.
- The number of radial nodes in an \(np\) orbital is given by \((n - l - 1)\), where \(l\) is the azimuthal quantum number.
- For \(p\) orbitals, \(l = 1\).
The plot shows:
- One radial node (the point where the probability density goes to zero). This indicates:
- For \(np\), the radial nodes = \(n - 1 - 1 = n - 2\).
- Setting the radial nodes to 1, we have \(n - 2 = 1\).
- Solving gives \(n = 3\).
Thus, the value of \(n\) corresponding to this plot of a \(np\) orbital is 3.
Conclusion: The correct answer is 3.
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