The energy spectrum of $$\beta $$-particles [ number $$N(E)$$ as a function of $$\beta $$-energy $$E$$ ] emitted from a radioactive source is

Starting with a sample of pure $${}^{66}Cu,{7 \over 8}$$ of it decays into $$Zn$$ in $$15$$ minutes. The corresponding half life is

If radius of the $$\matrix{ {27} \cr {13} \cr } $$ $$Al$$ nucleus is estimated to be $$3.6$$ fermi then the radius of $$\matrix{ {125} \cr {52} \cr } \,Te$$ nucleus is estimated to be nearly

The intensity of gamma radiation from a given source is $$L$$. On passing through $$36$$ $$mm$$ of lead, it is reduced to $${{\rm I} \over 8}.$$ The thickness of lead which will reduce the intensity to $${{\rm I} \over 2}$$ will be