Question

If uranium (mass number 238 and atomic number 92) emits an $\text{ }\alpha \text{ }$ particles, the product has a mass number and atomic number:
A) 236 and 92
B) 234 and 90
C) 238 and 90
D) 236 and 90

Answer 1

Hint: If an element emits an alpha particle the atomic mass of the element decreases by four-unit and atomic number by two units. The general depiction of the nuclear reaction is as follows,
$\text{ }_{b}^{a}\text{X}\to \text{ }_{d}^{c}\text{Y + }_{2}^{4}\text{He }$

Complete Solution :
Alpha particles are fast-moving particles that are made up of two protons and two neutrons ( a helium nucleus $\text{ }_{2}^{4}\text{He }$ ). They carry the $\text{ +2 }$ charge and strongly interact with the matter.
Uranium -238 or ${{\text{ }}^{\text{238}}}\text{U }$ is one of the most common isotopes of uranium. When uranium emits the alpha-particle such that its atomic number is decreased by two units and the mass number is reduced by four units. The general depiction of the nuclear reaction is as follows,
$\text{ }_{b}^{a}\text{X}\to \text{ }_{d}^{c}\text{Y + }_{2}^{4}\text{He }$
Where X is a radioactive species that emits the alpha particles and generates a new species Y . The nuclear reaction follows the conservation of mass and energy. The uranium emits an alpha particle.it the reaction is as shown below:
$\text{ }_{92}^{238}\text{U}\to \text{ }_{d}^{c}\text{Y + }_{2}^{4}\text{He }$
The reaction follows the conservation of mass. Thus the mass on the right-hand side is equal to the mass on the left-hand side. As follows,
$\begin{align}
& \text{ 238 = c + 4 } \\
& \therefore \text{c = 238} - 4 = 234 \\
\end{align}$
Thus the mass number of Y is 234.lets determine the atomic number of Y.As follows,
$\begin{align}
 & \text{ 92 = d + 2 } \\
 & \therefore \text{d} = 90 - 2 = 90\text{ } \\
\end{align}$
Thus the Y has an atomic mass of 234 and an atomic number of 90. The reaction of uranium is as shown below:
$\text{ }_{92}^{238}\text{U}\to \text{ }_{90}^{234}\text{Th + }_{2}^{4}\text{He }$
Therefore, the product has a mass number of 234 and an atomic number of 90.
So, the correct answer is “Option B”.

Note: Note that, the sum of the subscripts (that is atomic number and the atomic mass) is equal on the product and the reactant side. Nuclear reactions are said to follow the conservation of mass and energy. Therefore, in solving such a question, start with writing a reaction with emission of alpha, beta particles and then try to figure out the mass and an atomic number of the product.