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Quiz – Quantum numbers

Quantum numbers provide a detailed framework for describing the arrangement and behavior of electrons in atoms. Test your understanding of quantum numbers with a quiz.

Your turn – quantum numbers

  1. If \(n=5\), what are the possible values for \(\ell\)?

\(\ell\) can be \(0,\,1,\,2,\,3,\,4\).

  1. For a certain electron, \(\ell=0\). What is the shape of the subshell electron cloud of that electron?

\(\ell=0\) indicates an \(s\) orbital, which has a spherical shape.

  1. What are the \(n\) and \(\ell\) values for \(4d\) electrons?

\(n=4\) and \(\ell=2\)

  1. For an electron, the principle quantum number, \(n\) is \(3\). What are the possible values for \(\ell\) and \(m_{\ell}\)?

\(\ell\) can be \(0,\,1,\,2\).

For \(\ell=0\), \(m_{\ell}\) can be 0.

For \(\ell=1\), \(m_{\ell}\) can be \(0,\,+1,\,-1\).

For \(\ell=2\), \(m_{\ell}\) can be \(0,\,+1,\,-1\,\,+2,\,-2\).

  1. What are the names of the orbitals with the principle quantum number \(n=3\)?

\(\ell\) can be \(0,\,1,\,2\).

For \(\ell=0\), \(m_{\ell}\) can be 0. This indicates one orbital. Since \(n=3\), it is one \(3s\) orbital.

For \(\ell=1\), \(m_{\ell}\) can be \(0,\,+1,\,-1\). This indicates three separate orbitals. Since \(n=3\), it is three \(3p\) orbitals.

For \(\ell=2\), \(m_{\ell}\) can be \(0,\,+1,\,-1\,\,+2,\,-2\). This indicates five separate orbitals. Since \(n=3\), it is five \(3d\) orbitals.

  1. What are the possible values for \(\ell\), \(m_{\ell}\) and \(m_{s}\) for an electron in the \(n=1\) energy state?

\(\ell\) can be \(0\).

For \(\ell=0\), \(m_{\ell}\) can be 0. This indicates one orbital. Since \(n=1\), it is one \(1s\) orbital.

  1. How many valid combinations of quantum numbers exist for \(2p\) electrons?

For \(2p\) electrons:

  • \(n\) can only be \(2\), so it only has one possible value.
  • \(\ell\) can only be \(1\), so it only has one possible value.
  • For \(\ell=1\), \(m_{\ell}\) can be \(0,\,+1,\,-1\). It can have three possible values.
  • \(m_{s}\) can be \(-\frac{1}{2}\) or \(+\frac{1}{2}\). It can have two possible values.

Thus, the total number of valid combinations is \(1\times1\times3\times2=6\).

  1. Can an electron exist with \(n=4\), \(\ell=2\) and \(m_{\ell}=4\) quantum numbers? Explain, using possible quantum number combinations.

For \(n=4\), \(\ell\) can be \(0,1,2,3\). Therefore, \(\ell=2\) is valid.

For \(\ell=2\), \(m_{\ell}\) can be \(0,+1,-1,+2,-2\). \(m_{\ell}=4\) is not a possible value.

Therefore, \(n=4\), \(\ell=2\) and \(m_{\ell}=4\) is not a valid combination.

  1. Can two electrons have the following combination of quantum numbers?

    \(n=2\), \(\ell=0\) and \(m_{\ell}=0\)

Yes. One electron can have the upward spin (\(m_{s}=+\dfrac{1}{2}\)) and the other can have the downward spin (\(m_{s}=-\dfrac{1}{2}\)).

  1. Which type of orbital has the following combination of quantum numbers?

    \(n=4\), \(\ell=2\), and \(m_{\ell}=1\)

\(n=4\) means fourth shell.

\(\ell=2\) indicates the \(d\) orbital.

\(m_{\ell}\) can be \(0,+1,-1,+2,-2\), so there are five orbitals.

Therefore, \(n=4,\,\ell=2,\,m_{\ell}=1\) indicates one of the \(4d\) orbitals.

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