For a substance the average life for α- emission is 1620 years and for β-emission is 405 years. After how much  time the 1/4 of the material remains after α and β  emission?

λα=11620 per year and λβ=1405 per year and it is given that the fraction of the remained activity AA0=14Total decay constant λ=λα+λβ=11620+1405=1324per year We know that A=A0e-λt⇒t=1λlogeA0A⇒t=1λloge4=2λloge2=324 x 2 x 0.693                                           =449 years.