AP EAMCET Engineering 20 Apr 2019 Shift 2 Paper

The expression of the number of atom left undecayed is
N=N0(‌

1

2

)‌

t

T1∕2

‌‌‌‌.......(I)
The above expression for 20% decay is,
(1−‌

20

100

)N0=N0(‌

1

2

)‌

t1

18

0.8=(‌

1

2

)‌

t1

18

‌‌‌‌.......(II)
The equation (I) for 80% decay is
(1−‌

80

100

)N0‌‌=N0(‌

1

2

)‌

t2

18

0.2‌‌=(‌

1

2

)‌

t2

18

‌‌‌‌.......(III)
From equation (II) and (III)
4‌‌=(‌

1

2

)‌

t1−t2

18

log‌4‌‌=log(‌

1

2

)‌

t1−t2

18

log‌22‌‌=‌

t1−t2

18

‌log‌2‌

t2−t1

18

2‌‌=‌

t2−t1

18

t2−t1‌‌=36min