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  • A sample contains large number of nuclei. The probability that a nucleus in sample will decay after four half lives is-Option: 1 <img alt="\frac{1}{4

A sample contains large number of nuclei. The probability that a nucleus in sample will decay after four half lives is-

Option: 1

\frac{1}{4}


Option: 2

\frac{3}{4}


Option: 3

\frac{15}{16}


Option: 4

\frac{7}{16}


Answers (1)

Probability that a nucleus will not decay is-

\left(\frac{\mathrm{N}}{\mathrm{N}_0}\right)=\left(\frac{1}{2}\right)^{\mathrm{n}}=\mathrm{q}

When n is the no. of half lives

q=\left(\frac{1}{2}\right)^4=\frac{1}{16}

Probability that a nucleus will decay is

p=1-q=1-\frac{1}{16}=\frac{15}{16}

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Kshitij

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