You visited us 3 times! Enjoying our articles? Unlock Full Access!

Law of Conservation of Energy

Two identical...

Question

Two identical samples (same material and same material and same amount initially.) P and Q of a radioactive substance having mean life T are observed to have activities $A_{p}$ & $A_{Q}$ respectively at the time of observation. If P is older than Q, then the difference in their ages is:

T

(\frac{A_{P} - A_{Q}}{ℓ n 2})

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

T

(\frac{A_{P} + A_{Q}}{ℓ n 2})

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

T

(\frac{A_{Q} - A_{P}}{ℓ n 2})

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

None of these

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

Open in App

Solution

The correct option is A $T$ $(\frac{A_{P} - A_{Q}}{ℓ n 2})$
We know that
Average life is given by
$λ = \frac{1}{T}$
According to question we have
$A_{P} = A_{0} e^{- λ P}$ ---eq.1
$A_{Q} = A_{0} e^{- λ Q}$ ---eq.2
eq.1 / eq,2
$\frac{A_{P}}{A_{Q}} = e^{- λ (P - Q)}$
$ln \frac{A_{P}}{A_{Q}} = - λ (P - Q)$
$ln \frac{A_{P}}{A_{Q}} = - \frac{(P - Q)}{T}$
$P - Q = - T ln \frac{A_{P}}{A_{Q}}$
$P - Q = T ln \frac{A_{Q}}{A_{P}}$

Suggest Corrections

Similar questions

Q. For a radioactive material, its activity A and rate of change of its activity R are defined as

A = - \frac{d N}{d t}

and

R = - \frac{d A}{d t}

, where N(t) is the number of nuclei at time t. Two radioactive sources P(mean life

τ

) and Q (mean life 2

τ

) have the same activity at t = 0. Their rates of change of activitites at t = 2

τ

are R

_{P}

and R

_{Q}

, respectively. If

\frac{R_{P}}{R_{Q}} = \frac{n}{e}

, then the value of n is

Q. For a radioactive material, its activity

A

and rate of change of its activity

R

are defined as

A = \frac{- d N}{d t}

and

R = \frac{- d A}{d t}

, where

N (t)

is the number of nuclei at time

t

. Two radioactive sources

P

(mean life

τ

) and

Q

(mean life

2 τ

) have the same activity at

t = 0

. Their rates of change of activities at

t = 2 τ

are

R_{P}

and

R_{Q}

, respectively, If

\frac{R_{P}}{R_{Q}} = \frac{n}{e},

then the value of

n

is ____.

Q. If

a_{1}

a_{2}

a_{3}

, ... are in AP then

a_{p}

a_{q}

a_{r}

are in AP if

p, q, r

are in

Q. If

a_{1}, a_{2}, a_{3}, . . . . . . . . . .

are in AP then

a_{p}, a_{q}, a_{r}

are in AP if

p, q, r

are in:

Q. P and Q are points on sides AB and AC respectively of TriangleABC. If AP=3cm PB=6cm,AQ=5cm and QC=10cm.s.t BC=3PQ.

Join BYJU'S Learning Program

Two identical samples (same material and same material and same amount initially.) P and Q of a radioactive substance having mean life T are observed to have activities Ap & AQ respectively at the time of observation. If P is older than Q, then the difference in their ages is:

The correct option is A T (AP−AQℓn2)We know that Average life is given by λ=1TAccording to question we have AP=A0e−λP ---eq.1AQ=A0e−λQ ---eq.2eq.1 / eq,2APAQ=e−λ(P−Q)lnAPAQ=−λ(P−Q)lnAPAQ=−(P−Q)TP−Q=−TlnAPAQP−Q=TlnAQAP

Two identical samples (same material and same material and same amount initially.) P and Q of a radioactive substance having mean life T are observed to have activities $A_{p}$ & $A_{Q}$ respectively at the time of observation. If P is older than Q, then the difference in their ages is: