Question

Following a nuclear reaction, a nucleus of aluminum is at rest in an excited state represented by 27^13Al*

Answer 1

(a) E = hc / λ … 1.02 x 106 eV = 1240 / λ … λ = 1.2 x 10–3 nm

(b) p = h / λ … 6.63 x 10–34 / 1.2x10–12 m … = 5.43 x 10–22 kg-m/s

(c) From conservation of momentum, the momentum before is zero so the momentum after is also zero. To conserve momentum after, the momentum of the photon must be equal and opposite to the momentum of the Al nucleus. pphoton = pnucleus = malval … 5.43 x 10–22 = 4.48 x 10–26 val … val = 1.21 x 104 m/s

(d) K = ½ mv2 = ½ (4.48 x 10–26)(1.21 x 104)2 = 3.28 x 10–18 J