Question

State Pauli's exclusion principle and show that the
maximum number of electrons in a given shell is
2n2 where n is the principal quantum number of the
shell.

I need ANSWER ASAP​

Answer 1

Explanation:

Each shell can contain only a fixed number of electrons: The first shell can hold up to two electrons, the second shell can hold up to eight (2 + 6) electrons, the third shell can hold up to 18 (2 + 6 + 10) and so on. The general formula is that the nth shell can in principle hold up to 2(n2) electrons.

Answer 2

Let us look at the answer:

Explanation:

Pauli's exclusion principle states:

No, two electrons can have similar set of four quantum numbers.

The four quantum numbers give a complete address of an electron present in an element.

Principle quantum number (n) : main shell in which electron is present.

Azimuthal quantum number(l) : number of sub-shells present in main shell. Its value ranges from 0 to n-1.

For l=0, s-sub-shell

For  l=1, p-sub-shell

For l=2, d sub-shell

for l=3, f sub-shell.

Magnetic quantum number(m) : number of orbitals present in a subshell. Its value ranges from -l to +l

Spin quantum number (s) : magnetic spin of an electron. Its value can +1/2 or -1/2.  

So, let us take an example for the number of electrons present in n=3 that is  third shell.

n=3 , l=0, 1,2

for l=0 m=0  (one orbital)   s= +1/2 and -1/2    2 electrons

for l=1 , m = -1, 0,+1  (3 orbitals)                        6 electrons

for l=2, m = -2,-1,0, 1, 2  (5 orbitals)                 10 electrons

So, the total number of electrons present is 18. i.e. 2n² 2(3)² = 18