Q. The half life period of Pb^{210} is 22 years. If 2g of Pb^{210} is taken, then after 11 years the amount of Pb^{210} will be present is

(a) 0.1414g

(b) 1.414g

(c) 2.828g

(d) 0.707g

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Ans: (b)

Sol: N = N

_{0}(1/2)^{n}, Where n = t/T_{1/2}N/N_{0} = (1/2)^{n}

As , m ∝ N

m/m_{0} = (1/2)^{n}

m/2 = (1/2)1/2 = 1/√2

m= 2/√2

m = √2 = 1.414