You visited us 1 times! Enjoying our articles? Unlock Full Access!

Matter Waves

The activity ...

Question

The activity of a sample of a redioactive material is $A_{1}$ at time $t_{1} a n d A_{2}$ at time $t_{2} (t_{2} > t_{1})$ . if its mean life is T, then

A_{1} t_{1} = A_{2} t_{2}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

A_{2} = A_{1} e^{t_{1} - t_{2} / T}

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

A_{1} - A_{2} = t_{2} - t_{1}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

A_{2} = A_{1} e^{t_{1} / t_{2} T}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is C $A_{2} = A_{1} e^{t_{1} - t_{2} / T}$
$A_{1} = {(\frac{d N}{d t})}_{1}$

$= λ N_{1}$

$= λ N_{0} e^{- λ t_{1}}$

Similarily,

$A_{2} = {(\frac{d N}{d t})}_{2}$

$= λ N_{2}$

$= λ N_{0} e^{- λ t_{2}}$

Therefore,

$\frac{A_{2}}{A_{1}} = \frac{λ N_{0} e^{- λ t_{2}}}{λ N_{0} e^{- λ t_{1}}} = \frac{e^{- λ t_{2}}}{e^{- λ t_{1}}} = e^{(t_{1} - t_{2})} / T$

$\Rightarrow A_{2} = A_{1} e^{(t_{1} - t_{2})} / T$

So. the correct option will be $(B)$

Suggest Corrections

Similar questions

The activity of a radioactive sample is $A_{1}$ at time $t_{1}$ and $A_{2}$ at time $t_{2}$ . If τ is average life of sample then the number of nuclei decayed in time $(t_{2} - t_{1})$ is

Q. The activity of a radioactive sample is

A_{1}

at time

t_{1}

and

A_{2}

at time

t_{2}

. If

T_{a v}

is the average life time of the radioactive sample, then the number of atoms that decay during interval

(t_{2} - t_{1})

Q. The activity of a sample of a radioactive material is

A_{1}

at time

t_{1}

and

A_{2}

at time

t_{2} (t_{2} > t_{1})

. If its mean is life T, then

Q. The activity of a sample of a radio active material is

A_{1}

at time

t_{1}

and

A_{2}

at time

t_{2}

(

t_{2} > t_{1}

). If its mean life is

T_{1}

, then

Q. The activity of sample of radioactive materials is

A_{1}

at time

t_{1}

and

A_{2}

at time

t_{2} (t_{2} > t_{1})

. It's mean life is

T

, then

Join BYJU'S Learning Program

The activity of a sample of a redioactive material is A1 at time t1andA2 at time t2(t2>t1) . if its mean life is T, then

The correct option is C A2=A1et1−t2/TA1=(dNdt)1=λN1=λN0e−λt1Similarily,A2=(dNdt)2=λN2=λN0e−λt2Therefore, A2A1=λN0e−λt2λN0e−λt1=e−λt2e−λt1=e(t1−t2)/T⇒A2=A1e(t1−t2)/TSo. the correct option will be (B)

The activity of a sample of a redioactive material is $A_{1}$ at time $t_{1} a n d A_{2}$ at time $t_{2} (t_{2} > t_{1})$ . if its mean life is T, then