Question

Roughly speaking, the radius of an atom is about 10,000 times greater than that of its nucleus. If an atom were magnified so that the radius of its nucleus became 2.0 cm, about the size of a marble, what would be the radius of the atom in miles (1 mi 1609 m)?

Answer 1

Answer:

The radius of the atom in miles is 0.1243.

Explanation:

Given that radius of an atom is ten thousand times greater than of its nucleus.

$r=10000\times r_n$

$\frac{r}{r_n}=\frac{10,000}{1}$

r = radius of an atom

$r_n$ = radius of the nucleus

If the radius of the nucleus is magnified to 2 cm.

$R=2.0 cm$

$R_n=?$

Ratio of radius of an atom to the radius of the nucleus will remain constant:

$\frac{R}{R_n}=\frac{R}{2.0 cm}=\frac{10,000}{1}$

$R=20,000 cm=200 m$

1 mile = 1609 m

$200 m=\frac{1}{1609}\times 200 mile=0.1243 miles$

The radius of the atom in miles is 0.1243.