Question

which of the following is the atomic radius of chlorine if the internuclear distance between two chlorine atoms is 200 pm?
a 100 pm
b 196 pm
c 200 pm
d 90 pm

Explanation:

Step1: Recall atomic radius in diatomic molecule

In a diatomic molecule like \(Cl_2\), the internuclear distance is the sum of the atomic radii of the two chlorine atoms. Since both atoms are chlorine, their atomic radii are equal. Let the atomic radius of chlorine be \(r\). Then the internuclear distance \(d = r + r= 2r\).

Step2: Solve for atomic radius

We know \(d = 200\) pm and \(d = 2r\). So, we can solve for \(r\) by rearranging the formula: \(r=\frac{d}{2}\). Substituting \(d = 200\) pm, we get \(r=\frac{200\ \text{pm}}{2}= 100\ \text{pm}\).

Answer:

a. 100 pm