Question

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

Answer 1

Answer:

$R = 1.5* 10^{-10}m$

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

$\frac{2.5 * 10^{-11}m}{R} = \frac{1}{6}$

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: $1.5* 10^{-10}m$