Question

The luminous dials watches are usually made by mixing a zinc sulphide phosphor with an a-particle emitter. The mass of radium (mass number $226$ , half-life $1620 $ years) that is needed to produce an average of $10$ a-particles per second for this purpose is

• A. $2.77\, mg$
• B. $2.77 \,g$
• C. $2.77 \times 10^{-23}\, g$
• D. $2.77 \times 10^{-13} \,kg$

Answer 1

Answer: (D)

$\left|\frac{ d / N }{ dt }\right|=\lambda N$
Number of radius nuclei in $mg =\frac{ N _{ A } m }{226}$
Decay constant, $\lambda=\frac{0.693}{t_{1 / 2}}=\frac{0.693}{1620 \times 3.16 \times 10^7}$
$\left|\frac{ dN }{ dt }\right|=10=\frac{6.02 \times 10^{23} m }{226} \times \frac{0.693}{1620 \times 3.16 \times 10^7}$
$\therefore m =\frac{10 \times 226 \times 162 \times 3.16 \times 10^7}{6.02 \times 10^{23} \times 0.693}$
$=2.77 \times 10^{-10} g =2.77 \times 10^{-13} kg$