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. $2.77mg$
• B. $2.77g$
• 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, $\lambda =\frac{0.693}{t_{1/2}}=\frac{0.693}{1620\times 3.16\times 10^7}$
$\left|\frac{dN}{dt}\right|=10=\frac{6.02\times 10^{23}m}{226}\times \frac{0.693}{1620\times 3.16\times 10^7}$
$\therefore m=\frac{10\times 226\times 162\times 3.16\times 10^7}{6.02\times 10^{23}\times 0.693}$
$=2.77\times 10^{-10}g=2.77\times 10^{-13}kg$