Question

A hydrogen atom has a radius of 2.5 x 10-11 m
Determine the radius of a magnesium atom.

Answer 1

`R = 1.5* 10^(-10)m`

Step-by-step explanation:

Given

`r = 2.5 * 10^(-11)m` -- radius of hydrogen atom

See attachment

Required

Determine the radius of magnesium atom (R)

From the attachment, the ratio of a hydrogen atom to a magnesium atom is:

`Ratio = 6mm : 36mm`

Simplify

`Ratio =1 : 6`

Represent the radius as ratio:

`Ratio = r : R`

Substitute
`r = 2.5 * 10^(-11)m`

`Ratio = 2.5 * 10^(-11)m : R`

Equate both ratios

`2.5 * 10^(-11)m : R = 1 : 6`

Express as fraction

`(2.5 * 10^(-11)m)/(R) = (1)/(6)`

Cross Multiply

`R * 1 = 2.5 * 10^(-11)m * 6`

`R * 1 = 2.5 * 6* 10^(-11)m`

`R * 1 = 15* 10^(-11)m`

`R = 15* 10^(-11)m`

`R = 1.5*10* 10^(-11)m`

`R = 1.5* 10^(1-11)m`

`R = 1.5* 10^(-10)m`

Hence, the radius of the magnesium atom is:
`1.5* 10^(-10)m`