The quantum numbers of six electrons are given below. Arrange them in order of increasing energies. List if any of these combination(s) has/have the same energy(i) n = 4, l = 2, ml = -2, ms = -1/2(ii) n = 3, l = 2, ml = 1, ms = +1/2(iii) n = 4, l = 1, ml = 0, ms = +1/2(iv) n = 3, l = 2, ml = -2, ms = -111(v) n = 3, l = l, ml = -1, ms = +1/2(vi) n = 4, l = 1, ml = 0, ms = +1/2
Question
The quantum numbers of six electrons are given below. Arrange them in order of increasing energies. List if any of these combination(s) has/have the same energy(i) n = 4, l = 2, ml = -2, ms = -1/2(ii) n = 3, l = 2, ml = 1, ms = +1/2(iii) n = 4, l = 1, ml = 0, ms = +1/2(iv) n = 3, l = 2, ml = -2, ms = -111(v) n = 3, l = l, ml = -1, ms = +1/2(vi) n = 4, l = 1, ml = 0, ms = +1/2
Solution
The energy of an electron in an atom is primarily determined by the principal quantum number (n). The higher the value of n, the higher the energy. When two electrons have the same n, the azimuthal quantum number (l) comes into play. The higher the value of l, the higher the energy. The magnetic quantum number (ml) and the spin quantum number (ms) do not affect the energy of the electron.
So, based on the given quantum numbers, the electrons can be arranged in order of increasing energy as follows:
(iii) n = 4, l = 1, ml = 0, ms = +1/2 (vi) n = 4, l = 1, ml = 0, ms = +1/2 (i) n = 4, l = 2, ml = -2, ms = -1/2 (v) n = 3, l = 1, ml = -1, ms = +1/2 (iv) n = 3, l = 2, ml = -2, ms = -111 (ii) n = 3, l = 2, ml = 1, ms = +1/2
Electrons (iii) and (vi) have the same energy because they have the same quantum numbers.
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