Question

The atomic mass of Uranium \[{}_{92}^{238}{\text{U}}\] is \[238{\text{ - 0508 u}}\], while that of Thorium \[{}_{90}^{234}{\text{Th}}\] is \[234.0436\,{\text{u}}\], and that of Helium \[{}_2^4{\text{He}}\] is \[4.0026\,{\text{u}}\]. Alpha decay converts \[{}_{92}^{238}{\text{U}}\] into \[{}_{90}^{234}{\text{Th}}\] as shown below:
\[{}_{92}^{238}{\text{U}} \to {}_{90}^{234}{\text{Th}} + {}_2^4{\text{He}} + {\text{energy}}\]
Determine the energy released in this reaction.

Answer 1

Hint: First of all, we will calculate the atomic mass of the products, and then we will find the difference in the atomic masses between the products and the reactant. After that we will calculate the equivalent released by the calculated mass difference.

Complete answer:
Given:
Uranium atomic mass is \[238.0508\,{\text{u}}\]
Thorium atomic mass is \[{\text{234}}{\text{.0436}}\,{\text{u}}\]
Helium atomic mass is \[{\text{4}}{\text{.0026}}\,{\text{u}}\]
Reactants mass is \[{\text{238}}{\text{.0508}}\,{\text{u}}\]
We are asked to find the energy released in the reaction.
Mass of the products is given by:
\[{\text{234}}{\text{.0436}} + 4.0026 = 238.0462\,{\text{u}}\]
So, we calculate the mass difference of the reactants and the products by following:
\[\Delta m = 238.0508 - 238.0462 = 0.0046\,{\text{u}}\]
We know, one atomic mass unit is equivalent to \[931\,{\text{MeV}}\] .
So, the energy released in this reaction is:
$ = 0.0046 \times 931\,{\text{MeV}} \\
= 4.28\,{\text{MeV}} $

Hence, the energy released in the reaction is \[4.28\,{\text{MeV}}\] .

Additional information:
1. Uranium: With the symbol \[{\text{U}}\] and the atomic number \[92\] , uranium is a chemical element. It is a silvery-grey metal in the periodic table's actinide series. There are \[92\] protons and \[92\] electrons in the uranium atom, six of which are electrons for valence.
2. Thorium: Thorium, with the symbol \[{\text{Th}}\] and the atomic number \[90\] , is the weak radioactive metal element. When exposed to air thorium forming the thorium dioxide, Thorium is silver and tarnishes black; moderately hard and mixable, with a high melting point. Thorium is an electropositive actinide whose chemistry is influenced by the oxidizing state of \[ + 4\] ; it is very reactive and, when finely divided, can ignite through the air.
3. Helium: The symbol \[{\text{He}}\] and the atomic number \[2\] are a chemical element. The first in a noble gas group of the periodic table is colorless, odorless, tasteless, nontoxic, inert, monatomic gas. It boils the lowest of all components. Helium is the lightest second and richest element in the observable universe.

Note:
While solving this problem, we should know that the mass is converted into its equivalent energy as postulated by Einstein. This happens in case of radioactive elements where the nucleus can’t hold the excess mass of the element. Higher is the mass difference, greater is the energy produced.