Question

Suppose you take a trip to a distant universe and find that the periodic table there is derived from an arrangement of quantum mumbers different from the one on Earth. The rules in that universe are: 1. principal quantum number n = 1,2,... (as on Earth); 2. angular momentum quantum number = 0,1,2,...,n-1 (as on Earth); 3. magnetic quantum number me = 0,1,2,..., f (only positive integers up to and including are allowed); 4. spin quantum number m = -1,0, +1 (that is, three allowed values of spin). Assuming that the Pauli exclusion principle remains valid in the distant universe, what is the maximum number of electrons that can populate a given orbital there? maximum number electrons per orbital: 3 Write the electronic configuration of the element with atomic number 8 in the periodic table. Superscript numbers where appropriate but omit parentheses. electronic configuration: 1532s22p4 What is the atomic number of the second noble gas? atomic number: 10

Answer 1

The four set of quantum numbers are n, l, m_l and m_s​.

Here,

n = principal quantum number,

l = angular momentum quantum number,

m_l​ = magnetic quantum number

m_s​ = spin quantum number.

According to Pauli’s exclusion principle, no two electrons in an atom can simultaneously have the same set of four quantum numbers.

Part 1:

If the number spin quantum number has 3 values: -1, 0 and +1, then it will have 3 electrons of each spin in each orbital.

The maximum number of electrons that can populate a given orbital are 3.

Part 2:

Each orbital can occupy 3 electrons. Then s orbital also occupies 3 electrons then electronic configuration of the element with atomic number 8 becomes 1s³2s³2p².

Part 3:

For an element to behave as a noble gas it should have a completely filled orbital. Therefore, the first noble gas will have the configuration 1s³.

The second noble gas will have a completely filled 1s, 2s and 2p orbital and p orbital will have two sub-shells because for l = 1, m_l​ = 0 and 1.

So, its configuration = 1s³2s³2p⁶ and its atomic number is 12.

Part 1

The maximum number of electrons that can populate a given orbital are 3.

Part 2

Electronic configuration of the element with atomic number 8 is 1s³2s³2p².

Part 3

The atomic number of the second noble gas is 12.