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 alpha decay, releasing 5.3 MeV of energy. If the daughter product of this reaction is 92^x^236 (atomic mass = 236.04556), it will recoil away as the alpha particle leaves. Determine (a) the energy of the daughter product and (b) the energy of the alpha 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 emission. In addition, ignore relativistic effects. (a) Number Units (b) Number Units

Explanation / Answer

a)

md = mass of daughter product = 236.04556 u

vd = velocity of daughter product after decay

m = mass of parent

ma = mass of alpha particle = 4.0012 u

va = velocity of alpha particle after decay

using conservation of momentum

md vd = ma va

236.04556 vd = 4.0012 va

va = 59 vd eq-1

using conservation of energy

inital total energy when parent is at rest = KE of apha particle + KE of daughter product - 5.3 MeV

0 = (0.5) ma va2 + (0.5) md vd2 - (5.3) (106) (1.6 x 10-19)

using eq-1

0 = (0.5) (4.0012) (59 vd )2 + (0.5) (236.04556) vd2 - (5.3) (106) (1.6 x 10-19)

vd = 1.1 x 10-8 m/s

va = 59 vd = 59 (1.1 x 10-8) = 64.9 x 10-8 m/s

a)

Ed = energy of daughter product = (0.5) md vd2 = (0.5) (236.04556) (1.1 x 10-8)2 = 1.43 x 10-14 J = 0.0894 MeV

b)

Ea = energy of daughter product = (0.5) ma va2 = (0.5) (4.0012) (64.9 x 10-8 )2 = 8.43 x 10-14 J = 5.3 MeV

Related Questions

Navigate

• Browse (All)
• Browse R
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.