Saved Bookmarks
| 1. |
Two radioactive substances X and Y initially contain equal number of atoms. Their half-lives are 1 hour and 2 hours respectively. Calculate the ratio of their rates of disintegration after four hours. |
|
Answer» Solution :Rate of disintegration `(R)=(dN)/(dt)=lambdaN=Nxx0.693/T` `THEREFORE` The ratio of rates of disintegration , `R_1/R_2=(N_1/N_2)T_2/T_1` Here, `T_1`= 1 hour : `T_2` =2 hours `N_0` is same for both the RADIO ACTIVE substances. In four hours, X completes 4 half-lives as its half-life is 1 hour. The ramaining NUMBER of atoms of X, `N_1=N_0/2^n=N_0/2^4=N_0/16`. Y completes 2 half-lives in four hours as its half-life is 2 hours. The number of atoms of Y remaining , `N_2=N_0/2^2=N_0/4` `therefore R_1/R_2=N_0/16xx4/N_0(2/1)=1/2`. |
|