1. The radius of a Cl nucleus is 4.0 fm, and the radius of a Cl atom is 100 pm. (1 fm = 1x 10-15 m; 1 pm = 1 x 10-12 m).How many times larger is the diameter
of the Chlorine atom than the diameter of the Chlorine nucleus?

The diameter of the Chlorine atom is 25000 times larger than the diameter of the Chlorine nucleus.

Explanation:

From the question,

The radius of a Cl nucleus is 4.0 fm and radius of a Cl atom is 100 pm.

To determine how many times larger the diameter  of the Chlorine atom is than the diameter of the Chlorine nucleus,

First, we will determine the diameter of the Chlorine atom and the diameter of the Chlorine nucleus.

(NOTE: Diameter = Radius × 2)

For the Chlorine atom

Radius of the Chlorine atom = 100 pm

∴ Diameter of the Chlorine atom = 2 × 100 pm

Diameter of the Chlorine atom = 200 pm

For the Chlorine nucleus

Radius of Chlorine nucleus = 4.0 fm

∴ Diameter of the Chlorine nucleus= 2 × 4.0 fm

Diameter of the Chlorine nucleus = 8.0 fm

Now, we will convert both diameters ( diameter of Chlorine atom and diameter of Chlorine nucleus) to the same unit

For Chlorine nucleus

Diameter of the Chlorine nucleus = 8.0 fm

If 1 fm = 1 × 10⁻¹⁵ m

Then, diameter of the Chlorine nucleus = 8.0 × 1 × 10⁻¹⁵ m

Diameter of the Chlorine nucleus = 8.0 × 10⁻¹⁵ m

For Chlorine atom

Diameter of the Chlorine atom = 200 pm

If 1 pm = 1 × 10⁻¹² m

Then, diameter of the Chlorine atom = 200 × 1 × 10⁻¹² m

Diameter of the Chlorine atom = 200 × 10⁻¹² m

Diameter of the Chlorine atom = 2 × 10⁻¹⁰ m

Now, to determine how many times larger the diameter  of the Chlorine atom is than the diameter of the Chlorine nucleus, we will divide the diameter of the Chlorine atom by the diameter of Chlorine nucleus.

Diameter of Cl atom / Diameter of Cl nucleus = (2 × 10⁻¹⁰ m) / (8.0 × 10⁻¹⁵ m)

(2 × 10⁻¹⁰ m) / (8.0 × 10⁻¹⁵ m) = 25000

∴ Diameter of Cl atom / Diameter of Cl nucleus = 25000

Hence, the diameter of the Chlorine atom is 25000 times larger than the diameter of the Chlorine nucleus.

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explanation: