SATHEE: Atoms And Nuclei Question 393

Atoms And Nuclei Question 393

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

Options:

A) $2.77 m g$

B) $2.77 g$

C) $2.77 \times 10^{- 23} g$

D) $2.77 \times 10^{- 13} k g$

Show Answer

Answer:

Correct Answer: D

Solution:

$| \frac{d / N}{d t} | = λ N$

Number of radius nuclei in $m g = \frac{N_{A} m}{226}$

Decay constant, $λ = \frac{0.693}{t_{1 / 2}} = \frac{0.693}{1620 \times 3.16 \times 10^{7}}$

$| \frac{d N}{d t} | = 10 = \frac{6.02 \times 10^{23} m}{226} \times \frac{0.693}{1620 \times 3.16 \times 10^{7}}$
$∴ m = \frac{10 \times 226 \times 162 \times 3.16 \times 10^{7}}{6.02 \times 10^{23} \times 0.693}$ $= 2.77 \times 10^{- 10} g = 2.77 \times 10^{- 13} k g$

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Atoms And Nuclei Question 393

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

Options:

Answer:

Solution:

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