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Exercise:
Derive an expression for the number of orbitals for a given energy shell. What is the connection to the number of electrons per shell?

Solution:
For the energy shell with principal quantum number n there are n subshells with ell dots n-. For a given value of ell there are ell+ orbitals. The number of orbitals in the shell n is thus N _ell^n- left ell+ right This is the of an arithmetic sequence with n elements from to n-+ so N fracn+n-+ fracn^ n^ The number of electrons per shell follows from the fact that there can be two electrons per orbital so the maximum number of electrons per shell is N_e n^ For the first few shells we find N_e dots as expected.
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Exercise:
Derive an expression for the number of orbitals for a given energy shell. What is the connection to the number of electrons per shell?

Solution:
For the energy shell with principal quantum number n there are n subshells with ell dots n-. For a given value of ell there are ell+ orbitals. The number of orbitals in the shell n is thus N _ell^n- left ell+ right This is the of an arithmetic sequence with n elements from to n-+ so N fracn+n-+ fracn^ n^ The number of electrons per shell follows from the fact that there can be two electrons per orbital so the maximum number of electrons per shell is N_e n^ For the first few shells we find N_e dots as expected.
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Language
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Type
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