Get 2 FREE Instant-Explanations on Filo with code FILOAPP

Home

Nuclei of a radioactive {A} are being produceted at a constant

Question

Nuclei of a radioactive $A$ are being produceted at a constant rate a . The electro has a decay constant $λ$ . At time $t = 0$ there are $N_{0}$ nucleius of the element .
(a) calculate the number $N$ of nuclei of $A$ at same t
(b) if a = 2N_(0) lambda) $c a l c \underline{a} t e t h e ν m b e r o f ν c \leq i o f$ A $a f t e r o \neq = h a l f - l if e o f$ A $and t h e lim i t \in g v a l u e o f$ N $a s$ t rarr oo

Views: 975 students

Found 5 tutors discussing this question

Elizabeth Discussed

Nuclei of a radioactive

A

are being produceted at a constant rate a . The electro has a decay constant

λ

. At time

t = 0

there are

N_{0}

nucleius of the element .
(a) calculate the number

N

of nuclei of

A

at same t
(b) if a = 2N_(0) lambda)

c a l c \underline{a} t e t h e ν m b e r o f ν c \leq i o f

a f t e r o \neq = h a l f - l if e o f

and t h e lim i t \in g v a l u e o f

a s

t rarr oo

14 mins ago

Discuss this question LIVE

14 mins ago

Text solutionVerified

Answer: A::B::C::DSolution: Solution Image

Let at time

t

number of radioactive nuclie are

N

net rate of formation of nuclie of

A

\frac{d N}{d t} = a - λ, N or \frac{d N}{a - λ N} = d t

or \int_{N_{0}^{N} \frac{d N}{a - λ N} = \int_{0}^{1} d t}

Solving this equation , we get

N = \frac{1}{λ} [a - (a - λ N_{0}) e^{- λ t}]

Subsituting

a = 2 λ n_{0}

and

t = t_{1 / 2} = \frac{\in ( 2 )}{λ}

in equation (1),
we get ,

N = \frac{2}{3} N_{0}

(ii) subsitituting

a = 2 λ N_{0} and t \to \infty

equation (1) we get

N = \frac{a}{λ} = 2 N_{0}

Was this solution helpful?

150

Report

One destination for complete JEE/NEET preparation

One destination to cover all your homework and assignment needs

Learn Practice Revision Succeed

Instant 1:1 help, 24x7

60, 000+ Expert tutors

Textbook solutions

Big idea maths, McGraw-Hill Education etc

Essay review

Get expert feedback on your essay

Schedule classes

High dosage tutoring from Dedicated 3 experts

Trusted by 4 million+ students

Stuck on the question or explanation?

Connect with our physics tutors online and get step by step solution of this question.

231 students are taking LIVE classes

Question Text	Nuclei of a radioactive $A$ are being produceted at a constant rate a . The electro has a decay constant $λ$ . At time $t = 0$ there are $N_{0}$ nucleius of the element . (a) calculate the number $N$ of nuclei of $A$ at same t (b) if a = 2N_(0) lambda) $c a l c \underline{a} t e t h e ν m b e r o f ν c \leq i o f$ A $a f t e r o \neq = h a l f - l if e o f$ A $and t h e lim i t \in g v a l u e o f$ N $a s$ t rarr oo
Answer Type	Text solution:1
Upvotes	150

Text solutionVerified

Practice questions from similar books