# 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,

$$M_{(z)} = M_0 e^{-\lambda t}$$

$$\dfrac{M_0}{2} = M_0 e^{-\lambda (4)}$$

$$\Rightarrow \lambda = \dfrac{1}{4} \ln (2)$$

$$M_{(8)} = M_0 . e^{-\lambda . 8}$$

$$\Rightarrow M_{(8)} = M_0 . e^{-\dfrac{1}{4} . \ln (2) . 8}$$

$$M_{(8)} = M_0 e^{-2 \ln (2)}$$

$$M = \left(\dfrac{M_0}{4} \right)$$

$$= \dfrac{3.2 mg}{4}$$

$$M_{(8)} = 0.8 mg $$