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 …….

Options

A. 3
B. 5
C. 7
D. 9

Answer

C

Explanation

Volume of one silver atom `=(108)/(10.5) xx(1)/(6.022xx10^23)cm^3`
So, `4/3 pir^3 = (108)/(10.5)xx(1)/(6.022xx10^23)`
`=1.708xx10^(-23)`
`r^3 = 0.407xx10^(-23) cm^3`
`=0.407 xx10^(-29) m^3`
Area of each silver atom
`pir^2 = pi(0.407xx10^(-29)m^3)^(2//3)`
So , number of silver atoms in given area
`=(10^(-12))/(pi(0.407xx10^(-29)m^3)^(2//3))=(10^8)/(pixx2)`
`=1.6xx10^7=yxx10^x`
So, x = 7