Physics

Physics

Problem

For a radioactive material, its activity

A

and rate of change of its activity

R

are defined as

A = -\frac{dN}{dt}

and

R = -\frac{dA}{dt}

, where

N(t)

is the number of nuclei at time

t

. Two radioactive sources

P

(mean life

\tau

) and

Q

(mean life

2\tau

) have the same activity at

t = 0

. Their rates of change of activities at

t = 2\tau

are

R_P

and

R_Q

, respectively. If

\frac{R_P}{R_Q} = \frac{n}{e}

, then the value of

n

is [Adv.2015]

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