Given mass number of gold `= 197`, Density of gold `= 19.7 g cm^(-1)`. The radious of the gold atom is appoximately:

Options

A. `1.5 xx 10^(-8) m`
B. `1.5 xx 10^(-9) m`
C. `1.5 xx 10^(-10) m`
D. `1.5 xx 10^(-12) m`

Answer

C

Explanation

Volume occupied by one mole of gold
`= (197 g)/(19.7 km ^(-3)) = 10 c m ^(3)`
Valume of one atom
` = (10)/(6 xx 10^(-23)) = (5)/(3) xx 10^(23) xx 10^(23) c m ^(3)`
Let `r` be the radius of the atom . Therefore.
`(4)/(3) pi r ^(3) = (5)/(3) xx 10^(23) or r ~= 1.5 xx 10^(-10) m`