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The half life of Uranium - 233 is 160000 years, i.e., Uranium 233 decays at a constant rate in such a way that it reduces to 50% in 160000 years. In how many years will it reduce to 25% ? (a) 80000 years (b) 240000 years (c) 320000 years (d) 40000 years |
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Answer» (c) 320000 years Let the rate of decay of Uranium be R per cent per year. Also, let the initial amount of Uranium be 1 unit. Since, the half life of Uranium - 233 is 160000 years, therefore \(\big(1-\frac{R}{100}\big)^{160000}\) = \(\frac{1}{2}\) ..........(i) Suppose Uranium - 233 reduces to 25% in t years. Then, \(\big(1-\frac{R}{100}\big)^t\) = \(\frac{25}{100}\) = \(\frac{1}{4}\) = \(\big(\frac{1}{2}\big)^2\) = \(\Big(\big(1-\frac{R}{100}\big)^{160000}\Big)^2\) = \(\big(1-\frac{R}{100}\big)^{320000}\) \(\Rightarrow\) t = 320000 years. |
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