Question

Splitting a single Uranium-225 atom releases 3.24x10^ -11 J of energy.

A) The energy came from lost mass in the nuclei involed. Use Einstein's equation and this number to calculate how much mass the Uranium atom lost.

B)Imagine that in a particular nuclear chain reaction, each fission releases two neutrons that go on to split other atoms. In other words, at first only one atom is split, then in the second round 2 are split, in the third round 4 are split etc.. Using the number above for the amount of energy released in each particular splitting, how much energy would be released in the 20th round? The 40th round? The 100th round?

C) If each round takes 10^ -7 seconds ( a raesonable number - these things happen fast!0, how much power was released in the 40th round of fissions?

Answer 1

(A)

Mass lost of the atom = E/c²

c = 3* 10⁸ m/sec

E = 3.24* 10^-11 J

so, lost mass = 3.24* 10^-27 / 9

= 3.6 * 10^-28 kg

(B)

To split a single atom energy required = 3.24* 10^-11 J

atom split in the N^th round = 2^N-1

we generalize this by the question you can see in the first round 1 splitting and in the 2,3, 4 round 2,4,8 respectively

so, in the 20^th , 40^th and 100^th round split atoms are 2¹⁹ , 2³⁹ and 2⁹⁹

so the energy released in the  20^th round will be = 3.24* 10^-11 * 2¹⁹ J

=1.698 * 10^-5 J

so the energy released in the 40^th round will be = 3.24* 10^-11 * 2³⁹ J

= 17.81 J

so the energy released in the 100^th round will be = 3.24* 10^-11 * 2⁹⁹ J

= 2.05* 10¹⁹ J

(C)

each round takes 10^-7 seconds

Power released in the 40 th round of fission = E / t

= 18.41 / 10^-7

= 18.41*10⁷ W