Under certain circumstances, a nucleus can decay by emitting a particle more massive than an α-particle. Consider the following decay processes: Calculate the Q-values for these decays and determine that both are energetically allowed.

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Take a emission nuclear reaction: We know that: Mass of m1 = 223.01850 u Mass of m2 = 208.98107 u Mass of, m3 = 14.00324 u Hence, the Q-value of the reaction is given as: Q = (m1 − m2 − m3) c2 = (223.01850 − 208.98107 − 14.00324) c2 = (0.03419 c2) u But 1 u = 931.5 MeV/c2 ∴Q...
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Take a emission nuclear reaction: We know that: Mass of m1 = 223.01850 u Mass of m2 = 208.98107 u Mass of, m3 = 14.00324 u Hence, the Q-value of the reaction is given as: Q = (m1 − m2 − m3) c2 = (223.01850 − 208.98107 − 14.00324) c2 = (0.03419 c2) u But 1 u = 931.5 MeV/c2 ∴Q = 0.03419 × 931.5 = 31.848 MeV Hence, the Q-value of the nuclear reaction is 31.848 MeV. Since the value is positive, the reaction is energetically allowed. Now take a emission nuclear reaction: We know that: Mass of m1 = 223.01850 Mass of m2 = 219.00948 Mass of, m3 = 4.00260 Q-value of this nuclear reaction is given as: Q = (m1 − m2 − m3) c2 = (223.01850 − 219.00948 − 4.00260) C2 = (0.00642 c2) u = 0.00642 × 931.5 = 5.98 MeV Hence, the Q value of the second nuclear reaction is 5.98 MeV. Since the value is positive, the reaction is energetically allowed. read less
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