Video Transcript
Which of the following equations
represents the 𝛼 decay of radium-226?
To answer this question, we must be
able to identify 𝛼 decay, which is a type of radioactive decay where an 𝛼 particle
is ejected from the nucleus of a large unstable isotope, resulting in the formation
of a smaller, more stable isotope. An 𝛼 particle is composed of two
protons and two neutrons. We can represent this using nuclide
notation, where 𝐴 represents the mass number and where 𝑍 represents the number of
protons for nuclei or charge for particles. So, in nuclide notation, an 𝛼
particle can be represented using the chemical symbol for helium, He, which contains
two protons and has a mass number of four.
The question tells us that the
isotope undergoing 𝛼 decay is radium-226, which means that radium-226 must be a
reactant in this nuclear equation, and an 𝛼 particle, shown as a helium nucleus,
must be included in the products. So, we know that the correct answer
must feature radium-226 to the left of the arrow, which, according to the periodic
table, has 88 protons. And the correct answer should also
feature a helium nucleus in the products, to the right side of the arrow.
Using this information, we can
eliminate answer choice (A), which does feature radium-226 as a reactant particle
but has helium as a reactant instead of a product. We can eliminate answer choice (C)
for the same reason. We can also eliminate answer choice
(D), which features radium-226 as a product and not as a reactant. We can identify the correct answer
using the information that the total mass number of the reactants, represented again
here by 𝐴, must be equal to the total mass number of the products, while the total
number of protons in the reactants, represented here again by 𝑍, must be equal to
the total number of protons in the products. This will allow us to identify the
missing nucleus in the products.
The total mass number of the
reactants is equal to 226. So, we know that the sum of the
mass numbers of the products must also be equal to 226. We can solve for the missing mass
number by subtracting the mass number of an 𝛼 particle or helium nucleus, which is
four, from 226, which will give us a mass number of 222. So, we know that the missing
product must have a mass number of 222. We can repeat this process for
number of protons.
The total number of protons in the
reactants is 88. So, the total number of protons in
the products must also be equal to 88. So, we can find the number of
protons of the missing product by subtracting the number of protons in an 𝛼
particle or helium nucleus, which is two, from 88, which gives us 86. So, we know that the missing
product must have 86 protons. This also means that the missing
particle in the products has an atomic number of 86.
And if we look to the periodic
table to find atomic number 86, we will find the element radon, represented by the
chemical symbol Rn. So, we know that the correct answer
choice must feature radon-222 as a product particle. This means we can eliminate answer
choice (B), which does not feature radon-222 in the products. Therefore, the equation that
represents the 𝛼 decay of radium-226 is (E), where radium-226 decays to form
radon-222 plus helium nucleus or an 𝛼 particle.
