Question

If the ionic radius of M+
and X–
are respectively 135 pm and 209 pm, the expected value of atomic
radius of metal (M) and non metal (X) are respectively (X and M are elements of same period)
A) 180 pm & 90 pm
B) 135 pm & 209 pm
C) 90 pm & 180 pm
D) Same radius which is average of 135 pm & 209 pm
PLZ EXPLAIN

Answer 1

If the ionic radii of K^+ and F^- are about 1.34 A each, then the expected values of atomic radii of K and F should be respectively:

Answer 2

Answer:

The expected value of the atomic radius of $M^{+}$ = $180pm$.

The expected value of the atomic radius of $X^{-}$ = $90pm$.

Therefore, option A) $180 pm$ and $90pm$ is correct.

Explanation:

Data given,

The ionic radius of $M^{+}$ = $135pm$

The ionic radius of $X^{-}$ =  $209pm$

The expected value of the atomic radius of $M^{+}$ =?

The expected value of the atomic radius of $X^{-}$ =?

As we know,

• The atomic radius of the positive ion ( cation ) of an element is larger than the ionic radius. ( because cations are always shorter than the parent atoms ).
• Also, the more the positive ions pull the electrons closer. So the cation or the positive ion is smaller than the atom.

Similarly,

• The atomic radius of the negative ion ( anion ) of an element is smaller than the ionic radius. ( because anions are always larger than the parent atoms ).
• Also, the more the negative charge on the ion, the more the electrons repel each other.

Thus, the atomic radius of  $M^{+}$ should be greater than $135pm$.

And the atomic radius of  $X^{-}$ should be less than $209pm$.

After applying these conditions, let us check the options:

A) $180 pm$ and $90pm$

• $180 pm$ = greater than $135pm$.
• $90pm$ = less than $209pm$.

B) $135pm$ and $209pm$

• $135pm$ = equals to $135pm$.
• $209pm$ = equals to $209pm$.

C) $90pm$ and $180pm$

• $90 pm$ = less than $135pm$.
• $180pm$ = less than $209pm$.

D) The same radius which is an average of $135 pm$ & $209 pm$.

No, the radius of the ions cannot be the same.

Thus, from the above options, only option A) matches the criterion,

Therefore,

• The expected value of the atomic radius of $M^{+}$ = $180pm$.

• The expected value of the atomic radius of $X^{-}$ = $90pm$.