Question

Q.28. A chemistry instructor makes the following claim: "Consider that if the nucleus were the size of a grape, the electrons would be about 1 mile away on average." Is this claim reasonably accurate? Provide mathematical support.

Short answer

Answer

The claim is reasonably accurate.

Step-by-step solution

Step-by-Step Solution Step 1: Testing the accuracy of claim

The ratio of an atom to nucleus radius can be $\frac{{10}^{-10}m}{{10}^{-15}m}$. The ratio of the radius of the graph is 0.015 m to distance x.

Calculating the nucleus radio to the atom

On calculating the ratio of nucleus to atom:

$\frac{{10}^{-10}m}{{10}^{-15}m}=\frac{{10}^5}{1}$

On equation the ratio with graph ratio to distance:

$\frac{{10}^5}{1}=\frac{x}{0.015m}$

Calculating x (distance)

On calculating for x:

$$\begin{gathered} x=\frac{\left({10}^5\right)(0.015m)}{1} \\ x=1500m \\ x=0.932mi \\ x>>1mile \end{gathered}$$

The claim is accurate.