Silver (atomic weight `108 g mol^(-1))` has a density of `10.5 g cm^(-3)`. The number of silver atoms on a surfaces of area `10^(-12) m^(2)` can be expressed in scientific notation as `Y xx 10^(-x)`, The value of `x` is …….

Answer

7

Explanation

Volume of onemole of silver atoms `(108)/(10.5)cm^(3)//"mole"`
volume of one silver atom`=(108)/(10.5)xx(1)/(6.022x10^(23))cm^(3)`
so, `(4)/(3)piR^(3)=(108)/(10.5)xx(1)/(6.022xx10^(23))=1.708xx10^(-23)` [Neglecting the void space]
`R^(3)=0.407xx10^(-23)cm^(3),R^(3)=0.407xx10^(-29)m^(3)`
Area of each silver atom `piR^(2)=pixx(0.407xx10^(-29)m^(3))^(2//3)`
so, number of silver atoms in given area.
`=(10^(-12))/((0.407xx10^(-29)m^(3))^(2//3))=(10^(8))/((ppixx2))=1.6xx10^(7)=yxx10^(x)`