The principal quantum number (n):
1) specifies the subshell of the orbital.
2) specifies the principal shell of the orbital.
3) specifies the 3-D shape of the orbital.
4) specifies the maximum number of electrons.
5) none of the above
The correct answer is 2) specifies the principal shell of the orbital.
To understand this, let's break down the options:
1) The subshell of the orbital is determined by the azimuthal quantum number (l), not the principal quantum number (n). The azimuthal quantum number specifies the shape of the orbital within a given principal shell.
2) The principal quantum number (n) indeed specifies the principal shell of the orbital. It represents the energy level of an electron in an atom and determines its distance from the nucleus. Higher values of n correspond to higher energy levels and larger orbits.
3) The 3-D shape of the orbital is determined by both the azimuthal quantum number (l) and the magnetic quantum number (ml), not the principal quantum number (n). Different combinations of l and ml define the different subshells and their shapes.
4) The maximum number of electrons within a given shell (not a specific orbital) is determined by the formula 2n^2, where n is the principal quantum number. This means that the maximum number of electrons in the first shell (n=1) is 2, in the second shell (n=2) is 8, in the third shell (n=3) is 18, and so on.
Given the information above, the correct answer is option 2) the principal quantum number (n) specifies the principal shell of the orbital.