Answer:
[tex]R = 1.5* 10^{-10}m[/tex]
Explanation:
Given
[tex]r = 2.5 * 10^{-11}m[/tex] -- 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:
[tex]Ratio = 6mm : 36mm[/tex]
Simplify
[tex]Ratio =1 : 6[/tex]
Represent the radius as ratio:
[tex]Ratio = r : R[/tex]
Substitute [tex]r = 2.5 * 10^{-11}m[/tex]
[tex]Ratio = 2.5 * 10^{-11}m : R[/tex]
Equate both ratios
[tex]2.5 * 10^{-11}m : R = 1 : 6[/tex]
Express as fraction
[tex]\frac{2.5 * 10^{-11}m}{R} = \frac{1}{6}[/tex]
Cross Multiply
[tex]R * 1 = 2.5 * 10^{-11}m * 6[/tex]
[tex]R * 1 = 2.5 * 6* 10^{-11}m[/tex]
[tex]R * 1 = 15* 10^{-11}m[/tex]
[tex]R = 15* 10^{-11}m[/tex]
[tex]R = 1.5*10* 10^{-11}m[/tex]
[tex]R = 1.5* 10^{1-11}m[/tex]
[tex]R = 1.5* 10^{-10}m[/tex]
Hence, the radius of the magnesium atom is: [tex]1.5* 10^{-10}m[/tex]
