Two nuclei P and Q have equal number of atoms at t=0. Their half lives are 3 hrs and 9 hrs respectively. Compare their rates of disintegration after 18 hours form the starts.

Answer

`3:16`

Explanation

Number of half lives of P in 18 hours `=18/3=6`
Number of half lives of Q in 18 hours `=18/9=2`
Therefore, no. of nuclei left undecayed:
`N_(1)=N_(0)(1/2)^(6)=N_(0)//64`
`N_(2)=N_(0)(1/2)^(2)=N_(0)//4`
The ratio of their rates of disintegration is
`(R_(1))/(R_(2))=(lambda_(1)N_(1))/(lambda_(2)N_(2))=(T_(2))/(T_(1))((N_(1))/(N_(2)))=9/3xx(N_(0)//64)/(N_(0)//4)=3/16`
`3:16`