How many electrons have clockwise spin in a fully filled 4f sub shell and 3rd main shell?

Maximum number of orbitals in a shell = n2  (n= number of shell or principal quantum number)
Maximum number of electrons in a shell =  2n2 
Each orbital can have maximum of two electrons and they have to be in opposite spins.Thus for each orbital 1 electron will be in clockwise spin. Thus maximum number of electrons in clockwise spin would correspond to maximum number of orbitals available.
Thus maximum number of electrons with clockwise spin in a shell are = n2

Thus for 3rd (n=3)shell,  number of  electrons in clockwise spin = 3=9.

Number of orbitals in a subshell = 2l + 1 (where l is azimuthal quantum number)
For 4f subshell (l=3) Thus number of orbitals = 2×3 + 1 = 7
Maximum number of electrons in 4f orbital = 2×7 = 14
Thus on the same basis half of the electrons , i.e. 7 will have clockwise spin.

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4f sub shell have 7 electrons in clockwise if completely filled

and M-shell have 9 electrons if all the sub shells are completely filled.

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Thank you, ganesh max.

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