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How would rank these ions according to atomic radius: \[{K^ + },{\text{ }}C{a^{ + 2}},{\text{ }}{P^{ - 3}},{\text{ }}{S^{ - 2}},{\text{ }}C{l^ - }\] (from smallest to largest)? Please explain why you choose this order.

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Last updated date: 04th Mar 2024
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IVSAT 2024
Answer
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Hint: The atomic radius of an element is defined as the distance between the nucleus and the surrounding electron. The atomic radius varies differently along a period and along a group.

Complete step by step answer:
The atomic radius is a measure of the atomic size of an element. It is referred to as the distance between the centres of the nucleus and the outermost orbital of the atom. The outermost orbital means the orbital which contains the valence electrons.
The atomic radius of an atom depends on:
a. The number of electrons in the valence shell. The higher the number of electrons the longer is the outermost orbital from the nucleus.
b. The magnitude of the positive charge or number of protons. The greater the charge on an atom the higher is the attraction of the nucleus for the valence electron and shorter the atomic radius.
Let us consider the given ions and determine the number of electrons one by one.
\[{K^ + }\] : The atomic number is \[19\]. Thus by losing an electron the potassium ion gets a positive charge and the number of electrons is \[18\] and the number of protons is \[19\].
\[C{a^{ + 2}}\] : The atomic number is \[20\]. Thus by losing two electrons the calcium ion gets two positive charges and the number of electrons is \[18\] and the number of protons is \[20\].
\[{P^{ - 3}}\] : The atomic number is \[15\]. Thus by gaining three electrons the phosphorus ion gets three negative charges and the number of electrons is \[18\] and number of protons is \[15\].
\[{S^{ - 2}}\] : The atomic number is \[16\]. Thus by gaining two electrons the sulfur ion gets two negative charges and the number of electrons is \[18\] and the number of protons is \[16\].
\[C{l^ - }\] : The atomic number is \[17\]. Thus by gaining an electron the chloride ion gets a negative charge and the number of electrons is \[18\] and the number of protons is \[17\].
Hence all the given five ions have an equal number of electrons. So the atomic radius depends on the number of protons and the nuclear charge.
It is well known that the positively charged nuclei attract the negatively charged electron cloud towards itself. This leads to reduction in the atomic size and the atomic radius.
Thus the number of protons is in the order \[{P^{ - 3}},{\text{ }}{S^{ - 2}},{\text{ }}C{l^ - },{\text{ }}{K^ + },{\text{ }}C{a^{ + 2}}\]. So the \[C{a^{ + 2}}\] ion has the smallest size as the valence electrons feel more attraction by the nucleus due to more number of protons. Next is the \[{K^ + }\] ion followed by \[C{l^ - }\]ion and \[{S^{ - 2}}\]ion. The \[{P^{ - 3}}\] ion has the largest atomic radius due to more number of electrons than the number of protons.
Hence the order of atomic radius from smallest to largest is\[C{a^{ + 2}},{\text{ }}{K^ + },{\text{ }}C{l^ - },{\text{ }}{S^{ - 2}},{\text{ }}{P^{ - 3}}\] .

Note:
In the periodic table the elements are arranged in order of increasing atomic number. As phosphorus has the least atomic number and number of protons. So it is the largest. Calcium has the highest atomic number and has the most number of protons so it is the smallest.
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