1.

Find the half life of uranium, given that 3.23 xx 10^(-7)gm of radium is found per gm of uranium in old minerals. The atomic weight of uranium and radium are 238 and 226 and half life of radium is 1600 years :

Answer»

`4.70 xx 10^(7)"years"`
`4.70 xx 10^(8)"years"`
`4.70 xx 10^(9)"years"`
`4.70 xx 10^(10)"years"`

Solution :There exists a RADIOACTIVE equilibrium in very old minerals, so using the relation,
`lambda_(1)N_(1)=lambda_(2)N_(2)`
`lambda_(U)N_(U)=lambda_(R) lambda_(R)`
or `N_(U)/T_(U)=N_(R)/T_(R) or T_(U)=T_(R) (N_(U)/N_(R)) ........(1)`
Now, `N_(U) =(6.023 xx 10^(23))/(238)`
`and N_(R)=(6.023 xx 10^(23))/(226) xx 3.23 xx 10^(-7)`
`N_(U)/N_(R)=(226)/(238 xx 3.23 xx 10^(-7)) =2.94 xx 10^(6)`
From EQNS (1) and (2)
`T_U=1600 xx 2.94 xx 10^(6)=4.70 xx 10^(9)"years"`


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