When 8% of nuclei decays, then remaining nuclei are 92% from As, N=N0e−λt Here, N=0.92N0 So, 0.92N0=N0e−λt1 When, 77% nuclei decay remaining number of nuclei are 23%. So, ‌‌N=0.23N0 0.23N0=N0e−λt2 By dividing in equation (i) by equation (ii) ‌
0.92
0.23
=‌
e−λt1
e−λt2
=eλ(t2−t1) So, eλ(t2−t1)=4 By taking natural log of both sides λ(t2−t1)‌=ln‌4 ‌ and ‌t2−t1‌=12‌ minutes ‌ 12λ‌=2‌ln‌2 λ‌=‌
ln‌2
6
and relation between half life and decay constant is