InterviewSolution
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InterviewSolution
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Stationery nucleus `.^(238)U` decays by a emission generaring a total kinetic energy T: `._(92)^(238) rarr ._(90)^(234)Th +._2^4 alpha` What is the kinetic energy of the `alpha`-particle?A. slightly less than `T`B. `T//2`C. slightly less than `T`D. slightly greater than `T` |
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Answer» Correct Answer - C ( c) Let then kinetic energy of the `alpha-`particle be `E_alpha` and that of the thorium Th be `E_(Th)` The ratio of kinetic energies is `(E_alpha)/(E_(th)) = ((1)/(2) m_alpha v_alpha^2)/((1)/(2) m_(th) v_(th)^2) = ((m_alpha)/(m_(th))) ((v_alpha)/(v_(th)))^2` ....(1) By conservation of momentum the momentum of `alpha-`particle and that of the recoiling thorium must be equal. Thus, `m_alpha v_alpha = m_(th) v_(th)` or `(v_(alpha))/(v_(th)) = (m_(th))/(_(alpha))` ...(2) Subst. (2) into (1), we have `(E_(alpha))/(E_(th)) = ((m_alpha)/(m_(th)))((m_(th))/(m_(alpha)))^2 = (m_(th))/(m_(alpha)) = (234)/(4) = 58.5` Thus, the kinetic energy is the `alpha-`particle expressed as the fraction of the total kinetic energy `T` is given by `E_alpha = (58.5)/(1 + 58.5) T = (58.5)/(59.5) T = 0.98 T` which is slightly less than `T`. |
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