50% of the amount of a radioactive substance decomposes in 5 years. The time required for the decomposition of 99.9% of the substance will be

Here, half life, t1/2=5 yearsDecomposed amount = 99.9%Let the original amount, No = 100Left amount after time t,=100−99.9=0.1N = 0.1∵ kt=2.303log⁡N0N 0.693t1/2×t=2.303log⁡1000.1 0.693×t5=2.303log⁡103 t=2.303×3×50.693=49.85 years