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Half-lives of two radioactive elements A and B are 20 {~min} a

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Half-lives of two radioactive elements $A$ and $B$ are $20 min$ and $40 min$ , respectively. Initially, the samples have equal number of nuclei. After $80 min$ , the ratio of decayed numbers of $A$ and $B$ nuclei will be
(a) $1 : 16$
(b) $4 : 1$
(c) $1 : 4$
(d) $5 : 4$

Name: Video solution 1: Half-lives of two radioactive elements A and B are 20 min and 40 min, respectively. Initially, the samples have equal number of nuclei. After 80 min, the ratio of decayed numbers of A and B nuclei will be(a) 1:16(b) 4:1(c) 1:4(d) 5:4
Uploaded: 2022-07-12T09:12:36.000Z
Duration: 5 min
Description: Video solution 1: Half-lives of two radioactive elements A and B are 20 min and 40 min, respectively. Initially, the samples have equal number of nuclei. After 80 min, the ratio of decayed numbers of A and B nuclei will be(a) 1:16(b) 4:1(c) 1:4(d) 5:4

Views: 5,516 students

Updated on: Jan 6, 2023

Book:

Arihant Physics JEE Main Chapterwise Solutions (2019-2002) (Arihant)

Exam:

JEE Mains 2016

Found 3 tutors discussing this question

William Discussed

Half-lives of two radioactive elements

A

and

B

are

20 min

and

40 min

, respectively. Initially, the samples have equal number of nuclei. After

80 min

, the ratio of decayed numbers of

A

and

B

nuclei will be
(a)

1 : 16

(b)

4 : 1

(c)

1 : 4

(d)

5 : 4

13 mins ago

Discuss this question LIVE

13 mins ago

Text solutionVerified

Exp. (d)
Given,

80 min = 4

half-lives of

A = 2

half-lives of

B

.
Let the initial number of nuclei in each sample be

N

.
For radioactive element

A

N_{A}

after

80 min = \frac{N}{2 ^{4}}

\Rightarrow

Number of

A

nuclides decayed

= N - \frac{N}{16} = \frac{15}{16} N

For radioactive element

B

N_{B}

after 80 min.

= \frac{N}{2 ^{2}} \Rightarrow

Number of

B

nuclides decayed

= N - \frac{N}{4} = \frac{3}{4} N

∴

Ratio of decayed numbers of

A

and

B

nuclei will be

\frac{( 15/16 ) N}{( 3/4 ) N} = \frac{5}{4}

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Question Text	Half-lives of two radioactive elements $A$ and $B$ are $20 min$ and $40 min$ , respectively. Initially, the samples have equal number of nuclei. After $80 min$ , the ratio of decayed numbers of $A$ and $B$ nuclei will be (a) $1 : 16$ (b) $4 : 1$ (c) $1 : 4$ (d) $5 : 4$
Updated On	Jan 6, 2023
Topic	Nuclei
Subject	Physics
Class	Class 12
Answer Type	Text solution:1 Video solution: 2
Upvotes	273
Avg. Video Duration	3 min

Half-lives of two radioactive elements $A$ and $B$ are $20 min$ and $40 min$ , respectively. Initially, the samples have equal number of nuclei. After $80 min$ , the ratio of decayed numbers of $A$ and $B$ nuclei will be
(a) $1 : 16$
(b) $4 : 1$
(c) $1 : 4$
(d) $5 : 4$

Text solutionVerified

Filo tutor solutions (2)

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Half-lives of two radioactive elements A and B are 20 min and 40 min, respectively. Initially, the samples have equal number of nuclei. After 80 min, the ratio of decayed numbers of A and B nuclei will be(a) 1:16(b) 4:1(c) 1:4(d) 5:4

Text solutionVerified

Filo tutor solutions (2)

Questions from JEE Mains 2016 - PYQs

Practice questions from Arihant Physics JEE Main Chapterwise Solutions (2019-2002) (Arihant)

Practice more questions from Nuclei

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Half-lives of two radioactive elements $A$ and $B$ are $20 min$ and $40 min$ , respectively. Initially, the samples have equal number of nuclei. After $80 min$ , the ratio of decayed numbers of $A$ and $B$ nuclei will be
(a) $1 : 16$
(b) $4 : 1$
(c) $1 : 4$
(d) $5 : 4$