Video Transcript
Uranium-238 can produce a thorium
isotope when it emits an 𝛼 particle. Which of the following equations
correctly describes this transmutation process? (A) 238 92 U forms 236 90 Th plus 2
2 He. (B) 238 92 U forms 235 90 Th plus 3
2 He. (C) 238 92 U forms 234 92 Th plus 4
0 He. (D) 238 90 U forms 234 92 Th plus 4
2 He. Or (E) 238 92 U forms 234 90 Th
plus 4 2 He.
To answer this question, we need to
recall the composition of uranium-238 and 𝛼 particles and from there determine
which isotope of thorium is produced.
First, what is Z And A for
uranium-238? Since the element is uranium, it
will always have 92 protons, so Z is 92. Since we are told that it’s
uranium-238, this means that the mass number A is 238. We can then write uranium-238 in
the form 238 92 U. This is the symbol used for all
options apart from option (D). So we can determine that option (D)
cannot be the answer to this question.
Next, what is an 𝛼 particle? An 𝛼 particle is the nucleus of a
helium-4 atom. 𝛼 particles have a Z of two and an
A of four. Thus, an 𝛼 particle can be written
as 4 2 He. Only two of the answer choices use
this symbol, one of which is for option (D), which we’ve already determined to be
incorrect. The other is for option (E). Thus, we can already determine the
option (E) is the correct answer. But for completeness, let’s work
out what the thorium isotope will be.
To do this, we can use the equation
for nuclear reactions, where the total value for A and the total value for Z are the
same for reacting some products. From this, we make two equations:
one for Z and one for A. The equations show that the total
value for Z for the products is the same as the value of Z of the reactant. And the case is the same for A. We already know the values of Z and
A for uranium-238 and for the 𝛼 particles, and we want to find the values for
thorium. So we need to rearrange these
equations to make thorium the subject.
If we rearrange the equations,
substitute the values, and perform the calculations, we find that thorium has a
Z-value of 90, which makes sense as thorium has 90 protons, and that thorium has an
A-value of 234. So this thorium isotope can be
written 234 90 Th.
The only answer choice with this
symbol is option (E). Thus, we can be sure that the
equation that correctly describes this transmutation process is (E); 238 92 U forms
234 90 Th plus 4 2 He.
