Problem 9E

What is internal energy? Is internal energy a state function?

Solution: 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: Principal quantum number(n): This quantum number determines the main energy level in which the electron is present. Azimuthal quantum n umber( ): This quantum number determines the angular momentum of the electron. The v alue of 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 ………. Magnetic quantum number(m): This qlntum 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 , m have val es ranging from -l to . l Spin quantum number(m ): Thissuantum 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 Step1: a) For n = 3, the possible values of l are 0, 1 and 2 with designations s, p and d respectively. Since, the figure above is a dumbbell shaped orbital which is the shape of a p orbital, therefore the value of l for this orbital is 1. b) The value of n for the orbital is 3 and the value of l is 1. Thus, the designation of the orbital is 3p. c) As we move from lower energy level to higher energy level, the size of the orbital increases although the shape remains similar. So, the analogous orbital for n = 4 shell would be drawn larger. Thus, the correct option is (ii). --------------------