1.

For a substance the average life for `alpha-`emission is `1620` years and for `beta-`emission is `405` years. After how much time the `1//4` of the material remains after `alpha` and `beta` emission ?A. 1500 yearsB. 300 yearsC. 449 yearsD. 810 years

Answer» Correct Answer - C
( c) `lamda_alpha = (1)/(1620)` per year and `lamda_beta = (1)/(405)` per year and it is given that the fraction of the remained activity
`(A)/(A_0) = (1)/(4)`
Total decay constant
`lamda = lamda_alpha +lamda_beta = (1)/(1620) + (1)/(405) = (1)/(324)` per year
We know that `A = A_0 e^(- lamda t) rArr t = (1)/(lamda) log_e (A_0)/(A)`
`rArr t = (1)/(lamda) log_e 4 - (2)/(lamda) log_e 2 = 324 xx 2 xx 0.693`
=`449 years`.


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