Subshells of the Hydrogen Atom (a) Without referring to Table, predict the number of subshells in the fourth shell, that is, for n = 4. (b) Give the label for each of these subshells, (c) How many orbitals are in each of these subshells? a) What is the designation for the subshell with n = 5 and / = 1? (b) How many orbitals are in this subshell? (c) Indicate the values of ml for each of these orbitals.
Solution: Step1: In order to describe each electron in an atom in different orbitals(the region where probability of finding the electron is maximum), we need a set of four numbers known as quantum numbers. These are discussed below: a) Principal quantum number(n): This quantum number determines the main energy level in which the electron is present. b) Azimuthal quantum number(l): This quantum number determines the angular momentum of the electron. The value of l gives the subshell in a given principal energy level to which an electron belong. It can have positive integer values ranging from zero to (n - 1) where n is the principal quantum number. The various subshells or values of l are also designated by letters s, p, d, f,.....as Value of l 0 1 2 3 4 5 …….. Designation s p d f g h ………. c) Magnetic quantum number(m): Thilquantum number describes the behaviour of electron in a magnetic field. It gives the number of orbitals in a given subshell. For a given value of l ,l have values ranging from -l to +l. d) Spin quantum number(m ): Tss quantum number describes the spin orientation of an electron. Since, the electron can spin in only two ways- clockwise or anticlockwise, 1 1 therefore, the spin quantum number can have only two values: + 2 0r -2. Step2: a) For l = 1, the designation of the subshell is p. Thus, for n = 5 and l = 1, the designation of the subshell is 5p. Step3: b) For a given subshell l , there are (2 1) number of orbitals. Therefore, for = 1, number of orbitals = (2 x 1) + 1 = 2 + 1 = 3 Step4: c) For = 1, l = -1, 0, +1. -------------------