Question

Thorium (with half-life T_1/2 = 1.913 yr. and atomic mass 228.0287 u) undergoes alpha decay and produces radium (atomic mass 224.0202 u) as a daughter nucleus. (Assume the alpha particle has atomic mass 4.002603 u.)

1) What is the decay constant of thorium? (Note that the answer must be in units of hrs^-1.)

λ =

2) What percent of thorium is left after 200 days?

3) The energy released from the decay of 10 g of thorium is used to heat 3.8 kg of water (assume all the energy released goes into the water). What is the change in temperature of the water after 1 hr.?

ΔT =

Answer 1

= 1) = ln 2 tyr In 2 (1913 X 365x24 - 4.136 x 10 Shit 2) N = Next N -dt N. – (4-136X10](200X24) C C N N 0.82 - % of the left = 0.82x100 = 82% 3) Energy released per decay (228-0287 - 224-0202 -4.002603) X93)-5 MeV 5.493 M V No. of The atoms in 10g (N) = 10 X 6.02X1023 228 2.642 X 1022 AN IN = (4.136 X10 4(2.642X1024) Δt = 1.093 X 1018 decay/hr Total energy released pen hr = (1-093 x 10 18/85.493 MeV = 68 10 18 Me V = (6 x 1018) X 106x1.6x10487

960 000 1 ДТ - Да 160 000 60°C т C 3-8 Х4 200