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Half life of U-238 undergoing alpha decay is 4.5 xx 10^(9) years. What is the activity of one gram of U-238 sample ? |
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Answer» Solution : GIVEN ` T = 4.5 xx 10^(9) " YEAR1 year"=365.25 xx 8.64 xx 10^(4) s ` ` i.e,1 " year" = 3.156 xx 10^(7)_(s)` HENCE` T = 4.5 xx 10^(9) xx 3.156 xx 10^(7) s ` ` T = 14.202 xx 10^(16) s ` 238 g of Uranium consists of ` 6.023 xx 10^(23)`atoms 1 g ofUraniumconsists of ` ( 6.023 xx 10^(23))/238 ` atoms `i.e, N =0.0253 xx 10^(23)` atoms But activity A = ` lamda N " where"lamda = ( 0.693)/ T ` Hence `A =( 0.693 xx 0.0253 xx 10^(23))/(14.202 xx 10^(16))" dis.s"^(-1)` i.e, `A = 0.122 xx 10^(5) " dis.s"^(-1)` In terms of curie` A = ( 0.122 xx 10^(5))/(3.7 xx 10^(10)) Ci ` i.e, ` A = 0.03297 xx 10^(-5) Ci` `orA = 3.297 xx 10^(-7) C i` |
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