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 …….

Explanation

Volume of silver atoms `=4/3 pir^(3)`
Volume `=("Mass of one mole Ag atoms")/("Density of one mole Ag atoms")`
`4/3pir^(3)=((108 g " mol"^(-1)))/((10.5g cm^(-3))xx(6.022xx10^(23)" mol"^(-1)))`
`r^(3)=((108 g " mol"^(-1))xx3)/((10.5g cn^(-3))xx(6.022xx10^(23)" mol"^(-1))xx4xx3.142)`
`=4xx10^(-24)cm^(3)`
`r-(4xx10^(-24)cm^(3))^(1/3)=1.58xx10^(-8)cm=1.58xx10^(-10)m`
No. of silver atoms (n) on a surface area of `10^(-12)m^(2)` can be calculated as :
`(10^(-12)m^(2))=pir^(2)xxn`
`n=((10^(-12)m^(2)))/(3.142xx(1.58xx10^(-10)m)^(2))=0.127xx10^(8)`
`n=1.27xx10^(7)`
`yxx10^(x)=1.27xx10^(7) or x=7`