Final answer:
The number of electrons in an element with filled orbitals can be calculated using the electron configuration and the 2n² formula. The exact number depends on the specific configuration of filled and partially filled shells. Sodium, for instance, has three filled subshells and one partially filled subshell, corresponding to its known electron configuration.
Step-by-step explanation:
If all the orbitals shown in the three-dimensional model are filled, the number of electrons that this element has can be determined by the electron configuration and the formula 2n², which calculates the maximum number of electrons that can occupy a given shell (or energy level). For example, a filled n = 3 shell, as denoted in spectroscopic notation, is written as 3s²3p⁶3d¹⁰. When considering electron configurations, one must account for orbitals being filled in order of increasing energy, where before a given shell (such as n = 3) is fully occupied, electrons may begin filling the next shell (n = 4).
For instance, if shells 1 and 2 are full and shell 3 has nine electrons (option a), then the element would have a total of 29 electrons: (2*1²) + (2*2²) + 9 = 2 + 8 + 9 = 19. If shells 1, 2, and 3 are full and shell 4 has three electrons (option b), then the element would have a total of 39 electrons: (2*1²) + (2*2²) + (2*3²) + 3 = 2 + 8 + 18 + 3 = 31. Similarly, for options c and d, one could sum the full complement of electrons in the filled shells and add any electrons in partially filled shells or additional occupied shells.
Making sense of electron configurations is an essential part of understanding chemical properties and the periodic table. For example, sodium (Na) has three filled subshells (1s, 2s, 2p) and one partially filled (3s), aligning with its electron configuration 1s²2s²2p⁵3s¹.