MediumChemistryHigh School (11–12)Structure of the Atom › Quantum Mechanical Model of the AtomConceptual

Say which of these sets of quantum numbers (n, l, ml, ms) are not allowed, and why.

Try it on paper first. A hint, the key idea and the worked solution are here when you need them.

Say which of these sets of quantum numbers $(n, l, m_l, m_s)$ are not allowed, and why. For the allowed sets, name the orbital.

$(3, 3, 0, +\tfrac{1}{2})$ (b) $(4, 2, -2, -\tfrac{1}{2})$ (c) $(2, 0, 0, +1)$ (d) $(5, 3, +3, +\tfrac{1}{2})$ (e) $(1, 1, 0, -\tfrac{1}{2})$

Need a reminder? The key ideaShow

$n = 1, 2, 3, \ldots$ ; $l = 0$ to $n - 1$ ( $s, p, d, f$ ); $m_l = -l$ to $+l$ ; $m_s = \pm\tfrac{1}{2}$ . A subshell has $2l + 1$ orbitals and a shell $n^2$ . Nodes: radial $n - l - 1$ , angular $l$ , total $n - 1$ . With many electrons, orbitals fill in order of $(n + l)$ , the smaller $n$ first for a tie.

The worked solution

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Work it out on paper first. It is fine to get stuck or make a mistake: that is how we learn. When you are ready, go through the solution one step at a time, and check each step against your own.

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← Write all the allowed values of l and ml for the shell with n = 2.Find the number of radial nodes, angular nodes and total nodes of the orbitals 5p, 5d and 6s. →

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Say which of these sets of quantum numbers (n, l, ml, ms) are not allowed, and why.

The worked solution

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