A possible set of quantum numbers for the last electron added to complete an atom of potassium in its ground state is
a) n=4, l=0, ml=0, ms= -1/2
b) n=3, l=1, ml=0, ms= -1/2
c) n=4, l=1, ml=0, ms= +1/2
d) n=3, l=1, ml=1, ms= +1/2
e) n=4, l=2, ml=1, ms= +1/2
I want to say the answer is A because I got the quantum numbers
n =4, l=0, ml=0, ms =+1/2
However, answer choice A has the -1/2 for the magnetic spin. Is +1/2 correct for potassium?
Answer A. The sign for the electron spin is arbitrary, as the spin axis is arbitrary, if based on anything, it is an external magnetic field. There is no difference in energy levels, or order of filling the +- 1/2 spins.
Pls can u explain part of the answer seperate
You are correct that the correct set of quantum numbers for the last electron added to complete an atom of potassium in its ground state is:
n=4, l=0, ml=0, ms= -1/2
The quantum numbers represent different properties of an electron in an atom. The principal quantum number (n) represents the energy level or shell of the electron. The azimuthal quantum number (l) represents the subshell or orbital shape. The magnetic quantum number (ml) represents the orientation of the orbital in space, and the spin quantum number (ms) represents the direction of the electron's spin.
In the case of potassium, the atomic number is 19, which means it has 19 electrons. The electron configuration for potassium is 1s2 2s2 2p6 3s2 3p6 4s1. The last electron added to complete the atom of potassium is in the 4s orbital.
For the 4s orbital, the values for the quantum numbers are:
n=4, l=0, ml=0
The only difference in answer choice A is the value for ms. The spin quantum number represents the direction of the electron's spin, and it can be either +1/2 or -1/2.
Since the question asks for the electron in the ground state, and the electron in the 4s orbital is the last electron added to complete the atom, it follows the Pauli exclusion principle, which states that two electrons in the same orbital must have opposite spins. This means the ms value for the last electron in the 4s orbital should be -1/2, as given in answer choice A. So, the correct answer is A.
To determine the correct set of quantum numbers for the last electron added to complete an atom of potassium in its ground state, we need to consider the rules and constraints on quantum numbers.
The four quantum numbers are:
1) n (principal quantum number), which determines the energy level or shell of the electron.
2) l (azimuthal quantum number), which represents the shape of the orbital.
3) ml (magnetic quantum number), which indicates the orientation of the orbital within the subshell.
4) ms (spin quantum number), which describes the spin direction of the electron.
Let's analyze each answer choice and check if it meets the criteria for potassium in its ground state:
a) n=4, l=0, ml=0, ms= -1/2
This option is a valid set of quantum numbers. The principal quantum number (n) of 4 suggests that the electron is in the fourth energy level. The azimuthal quantum number (l) of 0 indicates an s orbital. The magnetic quantum number (ml) of 0 means the orbital is not oriented in any specific direction. Lastly, the spin quantum number (ms) of -1/2 indicates a spin-down electron. This set of quantum numbers is possible for potassium.
b) n=3, l=1, ml=0, ms= -1/2
This set of quantum numbers suggests that the electron is in the third energy level (n=3) and occupies a p orbital (l=1). However, the spin quantum number (ms) of -1/2 indicates a spin-down electron. Potassium's ground state would have a spin-up electron, so this option is not correct.
c) n=4, l=1, ml=0, ms= +1/2
Similar to option b, this set of quantum numbers suggests that the electron is in the fourth energy level and occupies a p orbital. However, as mentioned before, potassium's ground state would have a spin-up electron (ms=+1/2), so this option is not correct.
d) n=3, l=1, ml=1, ms= +1/2
This set of quantum numbers suggests that the electron is in the third energy level and occupies a p orbital, specifically the px orbital (ml=1). However, the spin quantum number (ms) of +1/2 indicates a spin-up electron, which is correct for potassium. So, this option is a possible set of quantum numbers.
e) n=4, l=2, ml=1, ms= +1/2
This set of quantum numbers suggests that the electron is in the fourth energy level and occupies a d orbital (l=2), specifically the dyz orbital (ml=1). However, the ground state of potassium only fills up to the 3p orbitals, so this option is not correct.
Based on the analysis, the correct answer is d) n=3, l=1, ml=1, ms=+1/2, since it represents a spin-up electron in the 3p orbital, which matches the characteristics of the ground state electron in potassium.