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How many p-orbitals are there in each period?
a. 1
b. 3
c. 5
d. 7
e. 14

I take this to mean "how many p-orbitals are there in each period of the periodic table?" Looking at the p-block on the periodic table, it looks like there are 6 elements with p-orbitals per period. This isn't an answer, so I'm a little lost.

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    $\begingroup$ The question you were asked is awkwardly stated, but if you recall that each orbital can accept two electrons you should be able to infer the number of p orbitals from your earlier observation. This number is equal to the number of allowable values of the magnetic quantum number $m$, for $l=1$ $\endgroup$ – Richard Terrett Nov 1 '13 at 1:31
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    $\begingroup$ Alright, so since p-orbitals require that l = 1, then the magnetic quantum number can assume 3 values (according to the equation x = 2l + 1), the values will be -1, 0, or 1. Therefore, the answer is 3. Thanks for the help! $\endgroup$ – Dave Nov 1 '13 at 1:48
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For the p subshell, the azimuthal quantum number, which describes the angular momentum and shape of the orbitals, is $l=1$. For the associated magnetic quantum number, discrete values in the range $-l, -l+1, ... 0 ..., l-1, l$ are allowed, so the number of different $m_l$ values is $2l+1$.

With $l=1$, it follows that there are $2 \cdot 1+1=3$ p orbitals with the $m_l$ values of -1, 0 and +1, respectively. Each orbital can hold 2 electrons, so the p subshell can contain a maximum of 6 electrons. This also explains why there are 6 elements in the p block of each period. With increasing atomic number $Z$, one p electron is added per element in this block.

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