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Answer to Question #92638 in Atomic and Nuclear Physics for Vaibhavi Desai

Question #92638
1. In a nuclear reaction, the mass of the reactant is 236.05 atomic units, and the mass of the product is 235.86 atomic units.

(1 atomic mass unit = 1.667 × 10^-27 kg).

Calculate the energy released in the process.

2. The isotope radium -226 has a half-life of 1600 years and suppose you had 1000 grams of radium -226

(i) How much would be left 4800 years?

(ii) Why would it be more of a problem to dispose radium-226 than an isotope of the same mass with a half-life of 10 years?
Expert's answer

1.

@$E=(m_1-m_2)c^2@$

@$E=(236.05-235.86)(1.667\cdot 10^{-27})(2.998\cdot 10^8)^2@$

@$E=2.85\cdot 10^{-11}J@$

2. i)

@$m=m_0 2^{-\frac{t}{T}}@$

@$m=(1000) 2^{-\frac{4800}{1600}}=125\ g@$

ii) It is because its half-life is greater. After 10 years we will have only 500 g of an isotope of the same mass. But we will have

@$m'=(1000) 2^{-\frac{10}{1600}}=996\ g@$

 of radium -226.

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