NEET Physics Nuclei Questions Solved

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

(a) 1500 years            (b) 300 years
(c) 449 years              (d) 810 years

(c) λα=11620 per year and λβ=1405 per year and it is given that the fraction of the remained activity AA0=14
Total decay constant
λ=λα+λβ=11620+1405=1324 per year
We know that A=A0e-λtt=1λlogeA0A 
t=1λloge4=2λloge2=324×2×0.693=449 year

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