MyQuestionIcon

1

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

Half Life and Average Life

Two radioacti...

Question

Two radioactive sample A and B have half $T_{1}$ and $T_{2}$ $(T_{1} > T_{2})$ respectively. At $T = 0$ , the activity of a B was twice the activity of A. Their activity will become equal after a time :

A

\frac{T_{1} T_{2}}{T_{1} - T_{2}}

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

B

\frac{T_{1} - T_{2}}{2}

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

C

\frac{T_{1} + T_{2}}{2}

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

D

\frac{T_{1} T_{2}}{12}

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

Open in App

Solution

The correct option is A $\frac{T_{1} T_{2}}{T_{1} - T_{2}}$
Consider initial activity of nuclei A and B be $A_{0}$ and $2 A_{0}$ respectively at a time $^{'} t^{'}$ their activity is given by:-
$A_{1} A_{0} e - λ t$ [for A ] $A_{2} = 2 A_{0} e - λ t$ [for B]
where $λ = \frac{l n 2}{T}$ [T=half -life]
When $A_{1} = A_{2}$ at time 't'
$= A_{0} e^{-} \frac{l n 2}{T_{1}} t = 2 A_{0} e^{-} \frac{l n 2}{T_{2}} t$ [ $λ_{1} = \frac{m_{2}}{T_{1}}$ and $λ_{2} = \frac{l n 2}{T_{2}}]$
Take log of both sides ,
$\frac{- m 2}{T_{1}} t = \frac{- m 2}{T_{2}} + l n 2$
$= \frac{- t}{T_{1}} = \frac{- t}{T_{2}} + 1$
$= t = \frac{T_{1} T_{2}}{T_{1} - T_{2}}$

Suggest Corrections

thumbs-up

0

Similar questions

Q. Two radioactive samples

A and B

have half lives

T_{1}

T_{2}

(T_{1} > T_{2})

respectively. At

t = 0

, the activity of

B

was twice the activity of

A .

Their activity will become equal after a time-

Q. Two radioactive samples

1

2

have half lives

T_{1}

T_{2} (T_{1} > T_{2})

respectively. At

t = 0

, the activity of

2

was twice the activity of

1

. Their activity will become equal after a time

Q. The half life of a radioactive sample is

T

. If the activities of the sample at time

t_{1}

t_{2}

(t_{1} < t_{2})

R_{1} and R_{2}

respectively, the number of atoms disintegrated in time

t_{2} - t_{1}

is proportional to,

Q. The activity of a sample is

A_{1}

t_{1}

A_{2}

t_{2}

t_{2} > t_{1}

). The half-life of sample is

T

. Then, the number of atoms that have disintegrated in time (

t_{1} - t_{2}

) is proportional to

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

A_{1}

t_{1}

A_{2}

t_{2}

t_{2} > t_{1}

). If its mean life is

T_{1}

View More

Join BYJU'S Learning Program

similar_icon

Related Videos

lock

Half and Average Life

PHYSICS

Watch in App

explore_more_icon

Explore more

Half Life and Average Life

Standard XII Physics

Join BYJU'S Learning Program

CrossIcon