One possible method for revealing the presence of concealed nuclear weapons is to detect the neutrons emitted in the spontaneous fission of ${ }^{240}Pu$ in the warhead. In an actual trial, a neutron detector of radius 1.0 m carried on a helicopter measured a neutron flux of  $50s^{-1}$ at a distance of $100m$  from a missile warhead. Estimate the mass of  ${ }^{240}Pu$ (in kg) in the warhead. The mean life for spontaneous fission in  ${ }^{240}Pu$ is  $6\times {10}^{18}\sec$ and 2.5 neutrons on an average are emitted in each fission (Avogadro’s number = $6\times {10}^{23}$ per mole).