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Radium 226 Ra , spontaneously decays to radon with the emission of an \alpha - particle and a \gamma ray. If the speed of the \alpha particle upon emission from an initially stationary radium nucleus is 1.5 ×107 m/s, what is the recoil speed of the resultant radon nucleus? Assume the momentum of \gamma ray is negligible compared to that of \alpha particle.

Option: 1

2.0 \times 10^5 \mathrm{~m} / \mathrm{s}


Option: 2

2.7 \times 10^5 \mathrm{~m} / \mathrm{s}


Option: 3

3.5 \times 10^5 \mathrm{~m} / \mathrm{s}


Option: 4

None of these


Answers (1)

best_answer

Conservation of linear momentum requires :

\mathrm{m}_{\text {radon }} \mathrm{v}_{\text {radon }}=\mathrm{m}_{\text {helium }} \mathrm{v}_{\text {helium }} 

with helium identified as the alpha particle. The nuclear masses can be approximated by

their mass numbers (222 and 4). Thus, the recoil speed of the radon is

(4 / 222) \times 1.5 \times 10^7 \mathrm{~m} / \mathrm{s}=2.7 \times 10^5 \mathrm{~m} / \mathrm{s} 

Posted by

manish painkra

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