Question

# Initial mass of a radioactive substance is 3.2 mg. It has a half-life of 4 h. Find the mass of the substance left undecayed after 8 h.

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#### Given data :-Initial Mass $$= M_0 = 3.2 mg$$$$t_{1/2} = 4 m$$To calculate , mass of the substance left undecayed after $$8h \, [M_z = 8]$$we know,$$M_{(z)} = M_0 e^{-\lambda t}$$$$\dfrac{M_0}{2} = M_0 e^{-\lambda (4)}$$$$\Rightarrow \lambda = \dfrac{1}{4} \ln (2)$$$$M_{(8)} = M_0 . e^{-\lambda . 8}$$$$\Rightarrow M_{(8)} = M_0 . e^{-\dfrac{1}{4} . \ln (2) . 8}$$$$M_{(8)} = M_0 e^{-2 \ln (2)}$$$$M = \left(\dfrac{M_0}{4} \right)$$$$= \dfrac{3.2 mg}{4}$$$$M_{(8)} = 0.8 mg$$

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