Question

1) A quantum harmonic oscillator with frequency ωcontains 41 electrons. What is the energy of the highest-energy electron? Assume that the electrons are in the lowest states possible.

2 a) An atom has a total of 18 electrons. What is the principal quantum number of the outermost shell?

2 b) How many electrons does the outermost shell shell contain?

3) Which of the following represents the possible range of integer values for the magnetic quantum number?

a) 1 to l

b) -n to +n

c) 0 to n

d) 0 to l

e) 1 to n

f) -l to +l

4) Suppose the orbital quantum number for an electron in the hydrogen atom is 4. How many orientations of the angular momentum vector are possible?

Answer 1

2 a) Given that an atom has a total of 18 electrons.

Electronic configuration = 1s² 2s² 2p⁶ 3s² 3p⁶

Hence, principal quantum number of the outermost shell = 3

b)  How many electrons does the outermost shell shell contain = 3s² 3p⁶ = 8

3) possible range of integer values for magnetic quantum number = -l to +l

4) Given that orbital quantum number for an electron in the hydrogen atom is 4.

i.e l = 4

no of orientations of the angular momentum vector = 2l+1 = 2.4 + 1 = 9