Question

4: electrons in atoms test - 11/14/2025
24 of 24
which of the following statements regarding the shapes and maximum electron capacities of s, p, d, and f orbitals are correct? (select all that apply.)
an s orbital can exist in multiple orientations, which allows it to hold a maximum of 6 electrons.
four of the d orbitals have a cloverleaf shape. a d orbital can hold a maximum of 10 electrons.
an s orbital has a spherical shape and can hold a maximum of 2 electrons.
an f orbital has a complex shape and can hold a maximum of 14 electrons.
a d orbital can hold a maximum of 10 electrons across its three orientations.
a p orbital has a dumbbell shape and can hold a maximum of 4 electrons across its three orientations.

Explanation:

• For the statement "An s orbital can exist in multiple orientations, which allows it to hold a maximum of 6 electrons":
• An s orbital has only one orientation (\(l = 0\), \(m_l=0\)). The maximum number of electrons in an s - orbital is \(2(2l + 1)=2\) (since \(l = 0\)), not 6. So this statement is incorrect.
• For the statement "Four of the d orbitals have a clover - leaf shape. A d orbital can hold a maximum of 10 electrons":
• There are five d - orbitals (\(l = 2\), \(m_l=- 2,-1,0,1,2\)). Four of them (\(d_{xy}\), \(d_{xz}\), \(d_{yz}\), \(d_{x^{2}-y^{2}}\)) have a clover - leaf shape and \(d_{z^{2}}\) has a different shape (two lobes along the z - axis and a donut - shaped ring in the \(x - y\) plane). The maximum number of electrons in a set of d - orbitals is \(2(2l + 1)=10\) (since \(l = 2\)). So this statement is correct.
• For the statement "An s orbital has a spherical shape and can hold a maximum of 2 electrons":
• The angular momentum quantum number \(l = 0\) for s - orbitals. The probability density function for an s - orbital is spherically symmetric. Using the formula \(N = 2(2l+1)\), with \(l = 0\), we get \(N = 2\). So this statement is correct.
• For the statement "An f orbital has a complex shape and can hold a maximum of 14 electrons":
• For \(l = 3\) (f - orbitals), \(m_l=-3,-2,-1,0,1,2,3\). The number of orbitals is \(2l + 1=7\). Using the formula \(N = 2(2l + 1)\), with \(l = 3\), we get \(N=14\). And f - orbitals have complex shapes. So this statement is correct.
• For the statement "A d orbital can hold a maximum of 10 electrons across its three orientations":
• There are five d - orbitals (\(l = 2\), \(m_l=-2,-1,0,1,2\)), not three. The maximum number of electrons in d - orbitals is \(10\) (from \(N = 2(2l + 1)\) with \(l = 2\)), but the number of orientations is five. So this statement is incorrect.
• For the statement "A p orbital has a dumbbell shape and can hold a maximum of 4 electrons across its three orientations":
• For \(l = 1\) (p - orbitals), \(m_l=-1,0,1\) (three orientations). Using the formula \(N = 2(2l + 1)\) with \(l = 1\), we get \(N = 6\) (since each of the three p - orbitals can hold 2 electrons). So this statement is incorrect.

Answer:

• "Four of the d orbitals have a cloverleaf shape. A d orbital can hold a maximum of 10 electrons."
• "An s orbital has a spherical shape and can hold a maximum of 2 electrons."
• "An f orbital has a complex shape and can hold a maximum of 14 electrons."