Chad's GC Video Quiz Question: Quantum Orbital

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quocstazz

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In chad 2012 GC quiz number 3 in the quantum number video. In the video, Chad talks about how to use n^2 (Where n is the shell number) to find how many possible orbital there are. I realized that when you try to use the same equation to find how many orbital there are in the 4th shell, the equation would tell you that there are only 16 orbitals. However, when i draw them out, i realize there are actually 18.

shell 1: 1s orbital
shell 2: 1s orbital 3p orbital
shell 3: 1s orbital 3p orbital
shell 4: 1s orbital 3p orbital 5d orbital
total: 18 orbitals total

am i missing something? Nonetheless, the equation works perfectly fine when looking for orbitals of shell 1 2 and 3.

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The equation is used to find the number of orbitals in each shell, not the cumulative sum.
shell 1: 1 s orbital
shell 2: 1 s orbital + 3 p orbitals= 4
shell 3: 1 s orbital + 3 p orbitals + 5 d orbitals=9
shell 4: 1 s orbital + 3 p orbitals + 5 d orbitals + 7 f orbitals=16.
 
The equation is used to find the number of orbitals in each shell, not the cumulative sum.
shell 1: 1 s orbital
shell 2: 1 s orbital + 3 p orbitals= 4
shell 3: 1 s orbital + 3 p orbitals + 5 d orbitals=9
shell 4: 1 s orbital + 3 p orbitals + 5 d orbitals + 7 f orbitals=16.

Thank you!

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