Final answer:
The 17th electron of Krypton has the four quantum numbers: principal quantum number (n=3), angular momentum quantum number (l=1), angular momentum projection quantum number (ml=0), and spin projection quantum number (ms=-1/2).
Step-by-step explanation:
The quantum numbers describe the state of an electron in an atom. Krypton (Kr) has an atomic number of 36, meaning the 17th electron is added in the process of building up the electron configuration from lower to higher energy states. Hence, we must fill the orbitals according to the Aufbau principle, taking into account Hund’s rule and the Pauli exclusion principle.
The electronic configuration of Krypton up to 17 electrons is 1s2 2s2 2p6 3s2 3p5. The 17th electron occupies the 3p orbital. The corresponding quantum numbers are the principal quantum number (n), angular momentum quantum number (l), angular momentum projection quantum number (ml), and spin projection quantum number (ms).
- Principal quantum number (n): Represents the energy level and for the 3p orbital, n is 3.
- Angular momentum quantum number (l): Relates to the shape of the orbital, which for p orbitals is 1.
- Angular momentum projection quantum number (ml): Can have values from -l to +l. Since there are 5 electrons in the 3p orbitals already, the 17th electron will have ml=0.
- Spin projection quantum number (ms): Can be either +1/2 or -1/2. Given the 17th electron is the last one to be added to that orbital and the first three p electrons would have filled the ml=-1,0,+1 with spins +1/2 respectively, the fourth electron would pair up with the electron with ml=-1 with spin -1/2, so the 17th electron should typically be in the ml=0 orbit with spin -1/2 as there's already an electron in ml=0 with spin +1/2.
So, the 17th electron of krypton has the quantum numbers (n=3, l=1, ml=0, ms=-1/2).