The initial number of atoms of a radioactive element with half life $100$ days, is $9.6×10_{26}$. The number of atoms remaining undecayed after $500$ days, will be

A

$9.6×10_{25}$

B

$3.84×10_{25}$

C

$3×10_{25}$

D

$19.2×10_{25}$

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Updated on : 2022-09-05

Solution

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Correct option is C)

Fraction undecayed after $500$ days is $=2_{(500/100)}9.6×10_{26} =329.6×10_{26} =3×10_{25}$