Question

Deep Space probes use the heat from the alpha decay of Pu -238 to generate electricity. The reaction is : Pu 94,238 gives off He 2,4 and U 92,234. the masses of the isotopes are:238.04956,4.00260, and 234.04095 amu, respectively. How much energy in KJ is possible from the decay of 25.0 mg of Pu 238?

Answer 1

First, identify how much mass is converted to energy:

Initial mass - Final mas = 238.04956 - (4.00260 + 234.04095) = 0.00601 amu

then...

this is per atomic mass unit

use a basis of --> grams

so

0.00601 grams are lost per mol of Pu...

mass = 0.00601 g = 0.00601*10^-3

so...

E = (mass)*c^2 = (0.00601*10^-3)(3*10^8)^2 = 540900000000 Joules per 0.00601

we have actually 25 mg ... so, relate

540900000000 J = 0.00601 grams

X energy = 25*10^-3

x = (25*10^-3 )/(0.00601 ) * 540900000000 = 2.25*10^12 J = 2.25*10^9 kJ per 250 mg of Pu