Shells are denoted by the letter \"n, \" which indicates the number of the shell

Question

Shells are denoted by the letter "n, " which indicates the number of the shell. How many orbitals are contained in the n = 1 shell? Subshells are sets of orbitals with the same n value and of the same type (s, d, or f). How many subshells does the n = 2 shell contain? How many orbitals are contained within the 2p subshell? How many orbitals are contained within the 3p subshell? 7. How many orbitals are contained within the 3d subshell? How many subshells does the n = 4 shell contain? How many orbitals are contained within the 4f subshell? How many orbitals are contained within the 3s subshell Examine the total number of orbitals in the n = 1 through 4 shells. What is the relationship between the n value and the total number of orbitals? number of orbitals = n number of orbitals = 2n number of orbitals = n^2

Explanation / Answer

1) n= shell no. (principal quantum no.),

if n= 1 , then value of l (ORBITAL ANGULR MOMENTUM QUANTUM NO.)= n-1=1-1= 0 ,

we know that 0=s,1=p,2=d,3=f,

n=1 , then s subshell = 1 orbital,

2) n=2 ,then l=2-1=1, 0,1,

0=s and 1=p,

then it contains 2 sub shells 2s and 2p,

3) n=4 , then l= n-1, l=4-1=3, values of l= 0,1,2,3 (upto 3),

then, it has 4 sub shells, 0=s,1=p,2=d,3=f,

that is 4s,4p,4d,4f,

4) 3s sub shell has 1 orbital, (no. of orbitals= magnetic quantum no.) (i.e values of magnetic quantum no.),

where n=3, l= 3-1=2, l= 0,1,2,

0=s, 3s , s, sub shell has 1 orbital,

ml=0 (magnetic quantum no.) (+l to -l)

5) 2p sub shell has 3 orbitals, (no. of orbitals= magnetic quantum no.) (i.e values of magnetic quantum no.),

n=2, l=2-1=1, l=0,1,

ml= +l to -l, (ml=magnetic quantum no.)

ml= +1,0,-1

1=p, then p has 3 orbitals,

6) 3p sub shell, where n=3, l= 3-1=2, (0,1,2),

l=1=p, ml= +l to -l, +1 ,0,-1,

therefore 3p sub shell has 3 orbitals (no. of orbitals= magnetic quantum no.) (i.e values of magnetic quantum no.),

7) 3d sub shell , where n=3, l=3-1=2,

l=0,1,2,

l= 2=d, ,

ml= + l to -l, +2,+1,0,-1,-2,

therefore 3d sub shell has 5 orbitals,

8) 4f sub shell , where n=4 , l=4-1=3, then,

l= 0,1,2,3,

3=f , ml= +l to -l , then,

ml= +3,+2,+1,0,-1,-2,-3,

there fore 4f sub shell has 7 orbitals,

9) n=1 , then total no. of orbitals are 1, that is n*n= total no. of orbitals,

1*1=1,

n=2, 2*2=4,

n=3, 3*3=9,

n=4, 4*4=16

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