## how many electrons in an atom could have these sets of quantum numbers?

Question

### Question:

How many electrons in an atom could have these sets of quantum numbers?

How many electrons in an atom could have these sets of quantum numbers?

(a) n= 2
(b) n= 4 l= 1
(c) n= 6 l= 3 ml= -1

Quantum Numbers:

The quantum numbers of an electron represent its shell, subshell, orbital, and spin in an atom.
Only certain values of the quantum numbers are possible, and the values of one quantum number are dependent on the value of the other one.

(a) n=2represents the second shell of the atom which has two subshells; s−and pp-subshells.
The ss-subshell has only one orbital while the pp-subshell has three orbitals.
Thus, a total of four orbitals are present which can contain a maximum of 4×2 = 8 electrons. So eight electrons can have this quantum number.

(b)n=4,l=1 designate the pp-subshell of the fourth shell which contains three 4p4p-orbitals. Thus, 3×23×2 = 66 electrons can have this set of quantum numbers.

(c) n=6,l=3,ml=−1 represents the ff-orbital of the 6f6f-subshell in the sixth shell.
Thus, there can only be two electrons having this set of quantum numbers.

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