Compare the atomic size of the following two magnesium isotopes: \({ }^{24} \mathrm{Mg}\) and \({ }^{26} \mathrm{Mg}\).

Short Answer

Expert verified
The atomic sizes of \(^{24}\mathrm{Mg}\) and \(^{26}\mathrm{Mg}\) are essentially the same because the atomic size is determined by the number of electron shells, not the number of neutrons. Both have the same number of electron shells, hence the same atomic size.

Step by step solution

01

Identify the Isotopes

Firstly, the two atoms to be compared are identified as different isotopes of magnesium: \(^{24}\mathrm{Mg}\) and \(^{26}\mathrm{Mg}\). They are isotopes because they have the same number of protons (which is the atomic number) but different number of neutrons.
02

Revisit the Atomic Structure

It's necessary to recall the basic atomic structure. The atomic size, or atomic radius, is determined by the area that surrounds the nucleus where there is a high probability of finding an electron. The number of electron shells primarily determine this, which are decided by the atomic number (number of protons).
03

Determine Atomic Size

Considering that the atomic number of magnesium is 12, both \(^{24}\mathrm{Mg}\) and \(^{26}\mathrm{Mg}\) have 12 protons and 12 electrons. As a result, they both have the same number of electron shells. The atomic size is mainly determined by the number of electron shells, not the number of neutrons.
04

Compare Atomic Sizes

Since \(^{24}\mathrm{Mg}\) and \(^{26}\mathrm{Mg}\) both have the same number of electron shells, they have essentially the same atomic size. The number of neutrons doesn't affect the atomic size, so the additional neutrons in \(^{26}\mathrm{Mg}\) do not make it larger than \(^{24}\mathrm{Mg}\).

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