Question

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

• A. $9.6\times {10}^{25}$
• B. $3.84\times {10}^{25}$
• C. $3\times {10}^{25}$
• D. $19.2\times {10}^{25}$

Answer 1

The correct option is C $3\times {10}^{25}$

Fraction undecayed after $500$ days is $=\frac{9.6\times {10}^{26}}{2^{\left(500/100\right)}}=\frac{9.6\times {10}^{26}}{32}=3\times {10}^{25}$