On breaking a cubic solid (edge = 1 m) into fine cubic particles of edge 1 μ m , surface becomes n × 100000 . The value of n is?

Step-by-step solution

For a cube of dimension ( 1 m × 1 m × 1 m ) , the surface area = ( 1 × 1 ) × 6 faces = 6 m 2 × 1 μ m 1 0 - 6 m 2 = 6 × 1 0 12 ( μ m ) 2 The volume =   1   m 3   ×   1μm 10 − 6 m 3 = 1 0 18 ( μ m ) 3 For 1 0 18 cubes of dimension ( 1 μ m × 1 μ m × 1 μ m ) , the total surface area = 1 0 18 × 1 μ m × 1 μ m × 6 f a c e s = 6 × 1 0 18 ( μ m ) 2 On breaking, the surface area becomes = 6 × 1 0 18 ( μ m ) 2 6 × 1 0 12 ( μ m ) 2 times = 1000000 times Hence n = 10