Question

Upon irradiating californium with neutrons, a scientist discovered a new nuclide having the mass number of $250$ and a half-life of $30$ min. After $90$min. of irradiation, the observed radioactivity due to nuclide was $100dis/min.$. How many atoms of the nuclide were prepared initially?

• A. $2.4\times {10}^4$
• B. $3.46\times {10}^4$
• C. $1900$
• D. $800$

Answer 1

Answer: (B)

$3.46\times {10}^4$

$\lambda t=ln\left(\frac{A_0}{A}\right)$ $=\frac{0.693}{30}\times 90=ln\frac{A_0}{A}=A_0=A\times 8$

$\therefore N_0=\frac{A_0}{\lambda }=\frac{800}{0.693}\times 30=3.46\times {10}^{4}atoms$

Hence option (B) is correct.