A small bottle contains powdered beryllium Be & gaseous radon which is used as a source of $\alpha$-particles. Neutrons are produced when $\alpha$-particles of the radon react with beryllium. The yield of this reaction is $\left(\frac{1}{4000}\right)$ i.e. only one $\alpha$-particle out of $4000$ induced the reaction. Find the amount of radon $\left(R{n}^{222}\right)$ originally introduced into the, source, if it produces $1.2\times {10}^6$ neutrons per second after $7.6$ days. $\left[T_{\frac{1}{2}}\right.$ of $R_n=3.8$ days]