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.

Question

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Answer 1

Given data :-
Initial Mass $= M_{0} = 3.2 m g$

$t_{1 / 2} = 4 m$

To calculate , mass of the substance left undecayed after $8 h [M_{z} = 8]$
we know,

$M_{(z)} = M_{0} e^{- λ t}$

$\frac{M _{0}}{2} = M_{0} e^{- λ (4)}$

$\Rightarrow λ = \frac{1}{4} ln (2)$

$M_{(8)} = M_{0} . e^{- λ . 8}$

$\Rightarrow M_{(8)} = M_{0} . e^{- \frac{1}{4} . l n (2) . 8}$

$M_{(8)} = M_{0} e^{- 2 l n (2)}$

$M = (\frac{M _{0}}{4})$

$= \frac{3 . 2 m g}{4}$

$M_{(8)} = 0.8 m g$

Answer 2

Given data :-

Initial Mass

= M_{0} = 3.2 m g

t_{1 / 2} = 4 m

To calculate , mass of the substance left undecayed after

8 h [M_{z} = 8]

we know,

M_{(z)} = M_{0} e^{- λ t}

\frac{M _{0}}{2} = M_{0} e^{- λ (4)}

\Rightarrow λ = \frac{1}{4} ln (2)

M_{(8)} = M_{0} . e^{- λ . 8}

\Rightarrow M_{(8)} = M_{0} . e^{- \frac{1}{4} . l n (2) . 8}

M_{(8)} = M_{0} e^{- 2 l n (2)}

M = (\frac{M _{0}}{4})

= \frac{3 . 2 m g}{4}

M_{(8)} = 0.8 m g