Review Conceptual Example 5 as background for this problem. Suppose some nucleus

Question

Review Conceptual Example 5 as background for this problem. Suppose some nucleus undergoes decay, releasing 5.2 MeV of energy. If the daughter product of this reaction is 92X236 (atomic mass = 236.04556) , it will recoil away as the particle leaves. Determine (a) the energy of the daughter product and (b) the energy of the particle (atomic mass = 4.002603 u). Assume that the energy of each particle is kinetic energy, and ignore any other small amounts of energy that might be carried away by other emissions. In addition, ignore relativistic effects.

Explanation / Answer

let

m1 = 4 amu

m2 = 236 amu

a) momentum gained by dauter product = momentum gained by alfa particle

m1*v1 = m2*v2

v1 = m2*v2/m1

= 236*v2/4

= 59*v2

Apply conservation of energy

(1/2)*m1*v1^2 + (1/2)*m2*v2^2 = 5.2 Mev

(1/2)*(m2/59)*(59*v2^2) + (1/2)*m2*v2^2 = 5.2 Mev

59*(1/2)*m2*v2^2 + (1/2)*m2*v2^2 = 5.2 Mev

60*KE_daughter = 5.2 Mev

KE_daughter = 5.2 Mev/60

KE_daughter = 0.087 Mev <<<<<<-----------------Answer

b) KE_alfa = 5.2 Mev - KE_daughter

KE_alfa = 5.2 MeV - 0.087

= 5.113 MeV <<<<<<-----------------Answer

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