Final answer:
The value of x, representing the number of neutrons released in the fission reaction of Plutonium-239, is 67. This was determined by using the conservation of nucleons in the reaction where Plutonium-239 absorbs a neutron and fissions to produce Cerium and Krypton.
Step-by-step explanation:
To find the value of x in the fission reaction where Plutonium-239 absorbs a neutron, we examine the equation:
^239_94Pu + ^1_0n → ^137_58Ce + ^{X}_{36}Kr + x^1_0n
To conserve the number of nucleons, the sum of nucleons before and after the reaction must be equal. Since a neutron has a mass number of 1, when it is absorbed by Plutonium-239 (which has a mass number of 239), the total number of nucleons goes up to 240. After fission, the resulting cerium (Ce) has a mass number of 137, and krypton (Kr) has a mass number supplied in the question as X. Adding the unknown number of neutrons released, we should arrive back at 240.
The equation for nucleon number conservation is:
240 = 137 + X + x
We are given that the mass number for Kr is 36, which means X = 36. Using this, we can find x.
240 = 137 + 36 + x
x = 240 - 137 - 36
x = 67
The value of x, the number of neutrons released, is 67.