Atoms And Nuclei Question 393
Question: The luminous dials watches are usually made by mixing a zinc sulphide phosphor with an $ \alpha $ - particle emitter. The mass of radium (mass number 226, half-life 1620 years) that is needed to produce an average of 10 $ \alpha $ -particles per second for this purpose is
Options:
A) $ 2.77mg $
B) $ 2.77g $
C) $ 2.77\times {{10}^{-23}}g $
D) $ 2.77\times {{10}^{-13}}kg $
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Answer:
Correct Answer: D
Solution:
- $ | \frac{d/N}{dt} |=\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}} $
$ | \frac{dN}{dt} |=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 $
