COMEDK Exam 2018 Solved Paper

Let initial masses of two radioactive substances be N0.
If T1 and T2 be the half-lives of two radioactive substances,
Then, ‌‌T1=1‌yr
T2=2‌yrs
Total time, t=6‌yrs
Hence, remaining mass of the first substances after
t‌=6‌yrs
N1‌=N0(‌

1

2

)‌

t

T

=N0(‌

1

2

)6∕1
‌=‌

N0

26

⇒‌‌N1‌=‌

N0

64

Similarly, remaining mass of the second substance after t=6 yrs
‌N2=N0(‌

1

2

)‌

t

T2

=N0(‌

1

2

)6∕2=‌

N0

8

⇒‌‌N2=‌

N0

8

∴‌‌

N1

N2

=‌

‌ N0 64 N0

8

=‌

1

8

⇒‌

N1

N2

=‌

1

8

. . . (i)
Since, activity, A=λN=‌

0.693

T

N
⇒A∝‌

N

T

∴‌‌

A1

A2

=‌

N1T2

N2T1

=‌

1

8

×‌

2

1

=‌

1

4

⇒A1:A2=1:4