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One reaction that occurs in nuclear power plants is given below:
[tex]\[
{}_{92}^{235} U + {}_0^1 n \rightarrow {}_{56}^{141} Ba + {}_{c}^{a} X + 3 \left( {}_0^1 n \right)
\][/tex]

The values of [tex]\(a, b, c,\)[/tex] and [tex]\(d\)[/tex] in the reaction above are:
(Record your four-digit answer in the numerical-response section below.)

Your answer: [tex]\(\square\)[/tex] [tex]\(\square\)[/tex] [tex]\(\square\)[/tex] [tex]\(\square\)[/tex]

Sagot :

GinnyAnsweridn
To solve for the values of [tex]\(a\)[/tex], [tex]\(b\)[/tex], [tex]\(c\)[/tex], and [tex]\(d\)[/tex] in the nuclear reaction:
[tex]\[ { }_{92}^{235} U + { }_0^1 n \rightarrow { }_{56}^{141} Ba + { }_{cd}^{ab} X + 3\left({ }_0^1 n\right) \][/tex]

we need to ensure the conservation of both atomic mass (A) and atomic number (Z).

First, let's conserve the atomic mass (A):
- The left side of the equation has [tex]\(235\)[/tex] (from uranium) + [tex]\(1\)[/tex] (from the neutron), giving a total atomic mass of [tex]\(236\)[/tex].
- The right side must also sum to this total mass: [tex]\(141\)[/tex] (from barium) + [tex]\(a\)[/tex] (from X) + [tex]\(3 \times 1\)[/tex] (from the three neutrons, each with atomic mass 1).

Thus, the equation for the conservation of atomic mass becomes:
[tex]\[ 235 + 1 = 141 + a + 3 \\ 236 = 141 + a + 3 \\ 236 = 144 + a \\ a = 236 - 144 \\ a = 92 \][/tex]

Now, let's conserve the atomic number (Z):
- The left side of the equation has [tex]\(92\)[/tex] (from uranium) + [tex]\(0\)[/tex] (from the neutron), giving a total atomic number of [tex]\(92\)[/tex].
- The right side must also sum to this total charge: [tex]\(56\)[/tex] (from barium) + [tex]\(c\)[/tex] (from X) + [tex]\(3 \times 0\)[/tex] (from the three neutrons, each with atomic number 0).

Thus, the equation for the conservation of atomic number becomes:
[tex]\[ 92 + 0 = 56 + c + 0 \\ 92 = 56 + c \\ c = 92 - 56 \\ c = 36 \][/tex]

Next, we need to identify [tex]\(b\)[/tex] and [tex]\(d\)[/tex] for element [tex]\( { }_{cd}^{ab} X \)[/tex]:
- Given [tex]\(a = 92\)[/tex] and [tex]\(c = 36\)[/tex], the element with atomic number 36 is Krypton (Kr).
- Thus, the mass number [tex]\(b\)[/tex] and the atomic number [tex]\(d\)[/tex] for Krypton are the same as those corresponding to the element's atomic number.

Therefore, the values are:
[tex]\[ a = 92 \\ b = 92 \\ c = 36 \\ d = 36 \][/tex]

So, the four-digit answer is:
[tex]\[ \boxed{9236} \][/tex]
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