Nuclear Physics And Radioactivity Question 257

Question: The half-life period of radium is 1600 years. The fraction of a sample of radium that would remain after 6400 years is [NCERT 1980; SCRA 1994; JIPMER 1997 CBSE PMT 1994; MNR 1998; MP PMT 2004; DPMT 2004]

Options:

A) $ \frac{1}{4} $

B) $ \frac{1}{2} $

C) $ \frac{1}{8} $

D) $ \frac{1}{16} $

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Answer:

Correct Answer: D

Solution:

Fraction $ =\frac{N}{N_{0}}={{( \frac{1}{2} )}^{\frac{6400}{1600}}}={{( \frac{1}{2} )}^{4}}=\frac{1}{16} $