Question

the total no.of atomic orbital in fourth energy level of an atom is

Answer 1

In nth shell the total no. Of subshells are n

eg 4th shell has 4 subshells-s(l=0),p(l=1),d(l=2),f(l=3) (here l is azimuthal quantam no.)

Total no of orbitals in a subshell with value of l=n are 2n+1 ..

Ex if l=3 then magnetic quantam no. Can have values from -3 to +3 (incld 0) that makes 7 orbitals in a subshell for l=3 … (now u can figure out why its 2n+1)

So lets begin with the ques..

4th shell has how many subshells? (Ans is 4)

Which subshells? S,p,d,f which have values of l as 0,1,2,3

Now for subshell s , how many orbitals are there ? (Use 2l+1 , here l=0 so total orbitals are 1 )

For subshell p there are 3 orbitals

For subshell d there are 5 orbitals

For subshell f there are 7 orbitals

Now add them up - u will get 16 orbitals

Now u r wondering then how came n^2..how it can give the desired result ..u can observe that the total orbitals (in the above ques) are given by : 1+3+5+7 (sum of first four odd nos)

U can simplify this result as total orbitals in nth shell is equal to sum of first n odd nos.

Now , if u know arithmetic progression u can figure it out that sum of first n odd nos is is n^2..

Answer 2

ANSWER

Solution:-

Number of atomic orbitals in an orbit =n

2

where, n = energy level

∴ Number of atomic orbitals in fourth energy level =4

2 =16

Hence, the total number of atomic orbitals in fourth energy level of an atom is 16...