The black discs x, y and z have radii 1 ~m , 2 ~m and 3 m respectively. The wavelengths corresponding to maximum intensity are 200 ~nm , 300 ~nm and 400 nm respectively. The relation between emissive power E _ x , E _ y and E _ z is

Step-by-step solution

array ll Emissive power E= A T^4 & E A T^4 A= R^2 & A R^2 array Given, R ₁=1 ~m , R ₂=2 ~m , R ₃=3 ~m A_x: A_y: A_z:: 1: 4: 9 By Wien's displacement law _ T = constant T 1 Given, aligned & _ 1 =200 ~nm , _ 2 =300 ~nm , _ 3 =400 ~nm & _x: _y: _z:: 2: 3: 4 & 1 ~T _x : 1 ~T _ y : 1 ~T _ z :: 2: 3: 4 aligned aligned & T_x: T_y: T_z:: 1 2 : 1 3 : 1 4 & or T_x: T_y: T_z:: 6: 4: 3...(ii) aligned Comparing the product AT ^4 for the 3 discs From (i) and (ii), we have, for disc x : A _ x T _ x ^4=1 (6)^4=1296 for disc y : A