Silver (atomic weight =108 ~g ~mol ⁻¹ ) has a density of 10.5 ~g ~cm ⁻³ . The number of silver atoms on a surface of area 10⁻¹² ~m ^2 can be expressed in scientific notation as y 10^x . The value of x is

Step-by-step solution

Volume of one mole of silver atoms = 108 10.5 ~cm ^3 / mole Volume of one silver atom = 108 10.5 1 6.022 10²³ ~cm ^3 So, aligned 4 3 R^3 & = 108 10.5 1 6.022 10²³ =1.708 10⁻²³ R^3 & =0.407 10⁻²³ ~cm ^3 & =0.407 10⁻²⁹ ~m ^3 aligned Area of each silver atom R^2= (0.407 10⁻²⁹ ~m ^3 )^ 2 / 3 So number of silver atoms in given area = 10⁻¹² (0.407 10⁻²⁹ ~m ^3 )^ 2 / 3 = 10^8 ( 2) =1.6 10^7=y 10^x so, x=7 Solid state Mathematical understanding III