Final answer:
The shell where the g subshell first occurs has 25 orbitals in total. This is because it contains s, p, d, f, and g subshells, which collectively account for 1, 3, 5, 7, and 9 orbitals respectively. The correct answer is option: C. 25
Step-by-step explanation:
The student asks about the number of orbitals in the shell where the g subshell first appears. To calculate this, we use the formula for the number of orbitals in a subshell, which is 2l + 1, where 'l' is the azimuthal quantum number associated with the subshell type (s, p, d...).
The s subshell has 'l' = 0, p has 'l' = 1, d has 'l' = 2, f has 'l' = 3, and by extension, the g subshell has 'l' = 4. For g orbitals, the number of orbitals is 2(4) + 1 = 9.
However, we are interested in the total number of orbitals in the shell where the g subshell first appears, which is the 5th shell. This shell will contain s, p, d, f, and g subshells.
The number of orbitals for each subshell in this shell would be:
- s subshell: 2(0) + 1 = 1
- p subshell: 2(1) + 1 = 3
- d subshell: 2(2) + 1 = 5
- f subshell: 2(3) + 1 = 7
- g subshell: 2(4) + 1 = 9
Total orbitals in the 5th shell = 1 + 3 + 5 + 7 + 9 = 25 orbitals. Therefore, the answer is Option C, which is 25 orbitals.