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GRE Subject Test: Chemistry : Filling Orbitals

Study concepts, example questions & explanations for GRE Subject Test: Chemistry

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Example Questions

Example Question #1 : Filling Orbitals

How many electrons can fit in the $\small n=3$ $\displaystyle \small n=3$ electron shell?

Possible Answers:

Eighteen

Six

Fourteen

Eight

Ten

Correct answer:

Eighteen

Explanation:

An $\small n=3$ $\displaystyle \small n=3$ shell contains 3s, 3d, and 3p subshells. Any s shell can hold up to two electrons, any p shell can hold six electrons, and any d shell can hold ten electrons.

This question is best solved by using quantum numbers. We are given the principle quantum number. Using this, we can work down to determine how many electrons can fit in this shell. The rules for quantum numbers are given below.

$n=\text{integer};\ 0<l<n-1;\ -l<m_l<l;\ m_s=\frac{1}{2}\text{or}-\frac{1}{2}$ $\displaystyle n=\text{integer};\ 0< l< n-1;\ -l< m_l< l;\ m_s=\frac{1}{2}\text{or}-\frac{1}{2}$

If the principle quantum number is three, then the next quantum number can be zero, one, or two. These correspond to the s, p, and d subshells, respectively.

$l=0\ (s),\ 1\ (p),\ 2\ (d)$ $\displaystyle l=0\ (s),\ 1\ (p),\ 2\ (d)$

After that, the next quantum number describes the orbitals within the subshells. Each orbital can carry two electrons, according to the final quantum number.

$l=0\ (s);\ m_l=0\rightarrow 2\ \text{electrons in the s subshell}$ $\displaystyle l=0\ (s);\ m_l=0\rightarrow 2\ \text{electrons in the s subshell}$

$l=1\ (p);\ m_l=-1,\ 0,\ 1\rightarrow 6\ \text{electrons in the p subshell}$ $\displaystyle l=1\ (p);\ m_l=-1,\ 0,\ 1\rightarrow 6\ \text{electrons in the p subshell}$

$l=2\ (d);\ m_l=-2,\ -1,\ 0,\ 1,\ 2\rightarrow 10\ \text{electrons in the d subshell}$ $\displaystyle l=2\ (d);\ m_l=-2,\ -1,\ 0,\ 1,\ 2\rightarrow 10\ \text{electrons in the d subshell}$

In total, there are eighteen electrons allowed in all subshells of the third energy level.

$\displaystyle 2+6+10=18$

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GRE Subject Test: Chemistry : Filling Orbitals

Study concepts, example questions & explanations for GRE Subject Test: Chemistry

All GRE Subject Test: Chemistry Resources

Example Questions

Example Question #1 : Filling Orbitals

All GRE Subject Test: Chemistry Resources

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