1.

Some amount of radioactive substance (half life =10 days) is spread inside a room and consequently the level of radiation becomes 50 times the permissible level for normal occupancy of the room. After how many days the room will be safe for occupation ?

Answer»

45.56 days
12.22 days
56.45 days
15.45 days

Solution :Let t be the required time to reach the permissible level, so activity will drop to `(1)/(50)` of its present VALUE after time t. Thus, if `R_(0)` be the present activity and R the activity remaining after time t, then
`R/R_(0)=1/(50) or N/N_(0)=1/(50) or e^(-lambdat)=(1)/(50)`
or `lambdat=log_(e) 50`
`or t=(log_(e)50)/(lambda) =(log_e 50 XX T)/(log_(e) 2)`
`or t=(1.6990)/(0.3010) xx 10" days "=56.45 days`


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