Multiple Choice
Which principal quantum number, n, corresponds to the orbit with the highest energy in a hydrogen atom?
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9. Quantum Mechanics
Quantum Numbers: Principal Quantum Number
Multiple Choice
Which of the following statements is true for an electron with principal quantum number n = 4?
A
The electron can be found in the 4s, 4p, 4d, or 4f subshells.
B
The maximum number of electrons in this shell is 16.
C
The possible values of the angular momentum quantum number l are 0, 1, and 2 only.
D
The principal quantum number n determines the shape of the orbital.
Verified step by step guidance1
Recall that the principal quantum number \(n\) defines the main energy level or shell of an electron in an atom. For \(n = 4\), the electron is in the fourth shell.
Determine the possible values of the angular momentum quantum number \(l\) for a given \(n\). The rule is \(l = 0, 1, 2, ..., (n-1)\). So for \(n = 4\), \(l\) can be 0, 1, 2, or 3.
Identify the subshells corresponding to each \(l\) value: \(l=0\) corresponds to the \(s\) subshell, \(l=1\) to \(p\), \(l=2\) to \(d\), and \(l=3\) to \(f\). Therefore, the \(n=4\) shell contains the 4s, 4p, 4d, and 4f subshells.
Calculate the maximum number of electrons in the \(n=4\) shell by summing the capacities of all its subshells. Each subshell can hold \$2(2l+1)\( electrons. So, total electrons = \)2(2*0+1) + 2(2*1+1) + 2(2*2+1) + 2(2*3+1)$.
Understand that the principal quantum number \(n\) primarily determines the energy level and size of the orbital, not its shape. The shape is determined by the angular momentum quantum number \(l\).
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