Question

1. What is the minimum value of l for a subshell that has 11 electrons in it?

2. If a hydrogen atom has its electron in the n = 6 state, how much energy in eV is needed to ionize it?

3. What is the smallest angle in degrees that S makes with the z -axis for an l = 1 electron?

Answer 1

1 Each subshell can hold only a fixed number of electrons in it.These subshells are named s,p,d,f,..etc                   s' subshell can hold 2 electrons, 'p' subshell can hold 6 electrons, d subshell can hold 10 electrons, 'f' subshell can hold 14 electrons. each of these subshells represent a value of 'l' that is ,                                                            l =0 means s subshell , l =1 means p subshell, l =2 means d subshell, l = 3 means f subshell. since we want a subshell to hold 11 electrons the minimum 'l' value is l=3, as it can hold 14 electrons.

2 Ionisation energy for hydrogen is given by Ei = - E0/ n^2   where E 0 is -13.6ev which is ground state energy of hydrogen. For n= 6 level we have Ei = - (-13.6)eV / (6)^2 = + 0.377eV.

3 The angle made by spin angular momentum vector S with z axis is given by the formula

                                                           cos = ms /       where spin quantum number s=1/2                         ms takes values from -s to +s

                                                            ms = 1/2  it is magnetic spin quantum number

                                                        cos = (1/2) /    cos = 0.577 = cos-1(0.577)

                                                         = 54.7 degree

when ms is +1/2 S makes 54.7deg with +z axis and when it is ms -1/2 S makes same angle with negative z axis.