The activity of a radioactive substance is $R_{1}$ at time $t_{1}$ and $R_{2}$ at time $t_{2}$ where $t_{2} > t_{1}$ .Its decay constant is $λ$ .Then the number of atoms decayed between the time interval $t_{1}$ and $t_{2}$ are

Question

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Answer 1

b'
Let $N_{1}$ be the number of atoms at $t_{1}$
$∴ R_{1} = λ N_{1}$
Let $N_{2}$ be the number of atoms at $t_{2}$
$∴ R_{2} = λ N_{2}$
$\Rightarrow R_{1} - R_{2} = λ N_{1} - λ N_{2}$
$\Rightarrow N_{1} - N_{2} = \frac{R _{1} - R _{2}}{λ}$
$∴$ number of atoms decayed between the time interval $t_{1}$ and $t_{2}$ are $\frac{R _{1} - R _{2}}{λ}$
'

Answer 2

b'

Let

N_{1}

be the number of atoms at

t_{1}

∴ R_{1} = λ N_{1}

Let

N_{2}

be the number of atoms at

t_{2}

∴ R_{2} = λ N_{2}

\Rightarrow R_{1} - R_{2} = λ N_{1} - λ N_{2}

\Rightarrow N_{1} - N_{2} = \frac{R _{1} - R _{2}}{λ}

∴

number of atoms decayed between the time interval

t_{1}

and

t_{2}

are

\frac{R _{1} - R _{2}}{λ}

'

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$\frac{l n ( 2 )}{λ} (R_{1} R_{2})$

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