1.

The half life period for a radioactive substance is 15 minutes.How many gms of this substance after one hour?

Answer»

25
46.875
43.75
37.5

Solution :Method-I:`Ao overset(15)tooverset(Ao)underset(2)-overset(30)tooverset(Ao)underset(4)-overset(45)tounderset(8)overset(Ao)tooverset(60)tounderset(16)overset(Ao)-`
After 60 MIN ,`(50)/(16)`=3.125 GRAM substance REMAINS.`therefore` 50-3.125=46.875 gram substance decay.
Method -II radioactive are ALWAYS first order reaction.
`therefore t_((1)/(2))=(0.693)/(K)`
`therefore K=(0.693)/(t_((1)/(2)))=(0.693)/(15)=0.0462"minute"^(-1)`
Now K=`(2.303)/(t)` log `([R]_(0))/([R]_(t))`
0.0462=`(2.303)/(60)` log `(50)/([R]_(t))`
`therefore` log50-log `[R]_(t)` =1.2036
log `[R]_(t)`=0.495
`[R]_(t)`=antilog 0.495`~~3.12`
`therefore` 50-3.12`~~`46.875 gram substance decay.


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