A small bottle contains powered beryllium Be & gaseous radon which is used as a source of `alpha`-particles. Netrons are produced when `alpha-`particles of the radon react with beryllium. The yield of this reaction is `(1//4000)` i.e. only one `alpha`-particle out of induced the reaction. Find the amount of radon `(Rn^(222))` originally introduced into the source, if it prouduces `1.2 xx 10^(6)` neutrons per second after `7.6` days. [`T_(1//2)` of `R_(n) = 3.8` days]

Answer

`3.3 xx 10^(-6) g`

Explanation

Let the amount of `R_(x)^(222)` be `N_(0), N_(7.6)=N_(0)/2^(2)=N_(0)/4`
Nuclei left after `7.6` day `=N_(0)/4`
Decay constant `=(ln 2)/t_(1//2)=0.693/(3.8xx24xx3600)//sec`
`lambda=2.11xx10^(-6) sec`
Activity `=N_(0)/4 lambda=` No. of `alpha` particles
No. of neitrons produced
`=(N_(0)xx2.11xx10^(-6))/(4xx4000)=1.2 xx10^(6)`
`N_(0)=9.095xx10^(15)` nuclei `=3.354xx10^(-4) g`