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JEE · NEET Previous Year Question

$Half life of radioactive element is 1600 years. The fraction of sample remains undecayed after 6400 years will be$

Topic: JEE PYQ

Answer: A. Full step-by-step solution below.

A $\frac{1}{16}$
B $\frac{1}{4}$
C $\frac{1}{8}$
D $\frac{1}{24}$

Correct answer: A

Solution

(a) T_{1/2} = 1600 years; T = 6400 years n = \frac{T}{T _{1/2}} = \frac{6400}{1600} = 4; N = N_{0} (\frac{1}{2})^{n} = N_{0} (\frac{1}{2})^{4}; \frac{N}{N _{0}} = \frac{1}{16}

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