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.
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,
$$M_{(z)} = M_0 e^{-\lambda t}$$
$$\dfrac{M_0}{2} = M_0 e^{-\lambda (4)}$$
$$\Rightarrow \lambda = \dfrac{1}{4} \ln (2)$$
$$M_{(8)} = M_0 . e^{-\lambda . 8}$$
$$\Rightarrow M_{(8)} = M_0 . e^{-\dfrac{1}{4} . \ln (2) . 8}$$
$$M_{(8)} = M_0 e^{-2 \ln (2)}$$
$$M = \left(\dfrac{M_0}{4} \right)$$
$$= \dfrac{3.2 mg}{4}$$
$$M_{(8)} = 0.8 mg $$