Question

Uranium-235 is a rare isotope of uranium that can be used for power plants as well as bombs. Its nucleus decays to a thorium-231 nucleus by emitting an α-particle. Uranium has atomic number 92, and thorium has atomic number 90. A nuclear reaction such as this is written using the following notation:

235U → 231Th + α

Mass number is the number of protons plus the number of neutrons. It is the top number in this notation. In these nuclear reactions, mass number is conserved. That is, the total number of protons plus the total number of neutrons must be the same on both sides of the reaction. Atomic number is the number of protons. It is the bottom number in this notation. Total charge must be conserved. That means that total number of protons minus the total number of electrons must be the same on both sides of the reaction.

Problem 1 Knowing that there are no electrons in an α-particle, deter- mine the mass number and atomic number of an α-particle.

(a) 2α (b) 4α (c) 24α (d) 42α

Problem 2 The mass of uranium-235 is 235.044 amu. The mass of thorium-231 is 231.036 amu. The mass of an α-particle is 4.002 amu. Use conservation of energy and conservation of momentum to determine the ki- netic energy of the thorium nucleus and the kinetic energy of the α-particle. Work in the rest frame of the uranium nucleus (that means assume that the uranium nucleus is at rest).

Answer 1

Solution 1:

As the mass number is conserved in a nuclear reaction. Total mass number before the nuclear reaction is equal to total mass number after the nuclear reaction.

So, mass number of Uranium = mass number of Thorium + mass number of alpha particle

Therefore, 235 = 231 + mass number of alpha particle

mass number of alpha particle = 235 - 231 = 4

Total number of protons in an atom = atomic number of atom.

number of protons of Uranium = number of protons of Thorium + number of protons of alpha particle

Atomic number of Uranium = Atomic number of Thorium + Atomic number of alpha particle

92 = 90 + atomic number of alpha particle

Atomic number of alpha particle = 92 - 90 = 2

So, the mass number is 4 and atomic number is 2 of an alpha particle i.e. option (b) is correct.