Question 271: Atoms & Nuclei

Question

Half lives of two radioactive nuclei A and B are 10 minutes and 20 minutes, respectively, If initially a sample
has equal number of nuclei, then after 60 minutes, the ratio of decayed numbers of nuclei A and B will be :

Accepted Answer

N
A
= N
0
$${\left( {{1 \over 2}} ight)^{{t \over {{T_{{1 \over 2}}}}}}}$$
=  N
0
$${\left( {{1 \over 2}} ight)^{{{60} \over {10}}}}$$
=  N
0
$${\left( {{1 \over 2}} ight)^6}$$
N
B
= N
0
$${\left( {{1 \over 2}} ight)^{{t \over {{T_{{1 \over 2}}}}}}}$$
=  N
0
$${\left( {{1 \over 2}} ight)^{{{60} \over {20}}}}$$
=  N
0
$${\left( {{1 \over 2}} ight)^3}$$
Decayed nuclei of A = N
0
- N
0
$${\left( {{1 \over 2}} ight)^6}$$
Decayed nuclei of B = N
0
- N
0
$${\left( {{1 \over 2}} ight)^3}$$
$$ 	herefore $$ Ratio = $${{{N_0} - {N_0}{{\left( {{1 \over 2}} ight)}^6}} \over {{N_0} - {N_0}{{\left( {{1 \over 2}} ight)}^3}}}$$
= $${{{N_0}\left( {1 - {1 \over {{2^6}}}} ight)} \over {{N_0}\left( {1 - {1 \over {{2^3}}}} ight)}}$$
= $${{\left( {{{63} \over {{2^6}}}} ight)} \over {\left( {{7 \over {{2^3}}}} ight)}}$$
= $${9 \over 8}$$

Answer

9 : 8

Answer

1 : 8

Answer

8 : 1

Answer

3 : 8

Atoms & Nuclei

Half lives of two radioactive nuclei A and B are 10 minutes and 20 minutes, respectively, If initially a sample has equal number of nuclei, then after 60 minutes, the ratio of decayed numbers of nuclei A and B will be :

Choose the correct answer: