Compete the following nuclear equation:
235 4
92 u----> 2 He
a
Pa-231
b
U-235
c
Th - 231
d
Ac - 231
b. U-235
√50 over 2-√3
To rationalize the denominator (i.e., get rid of the radical in the denominator), we'll multiply both the numerator and denominator by the conjugate of the denominator, which is 2+√3:
√50 over 2-√3 * 2+√3 over 2+√3
Simplifying the numerator and denominator, we get:
(√50 * (2+√3)) / (4-3)
The denominator simplifies to 1, and we can simplify the numerator by multiplying the term inside the square root by 2:
(√100 * √3 + √50) / 1
Now we can just simplify further:
(10√3 + √50)
The correct completion for the given nuclear equation is:
a) Pa-231
To complete the given nuclear equation, we need to balance the number of protons and neutrons on both sides of the equation.
The given equation is:
235 4
92 U ---> 2 He
In this equation, the uranium isotope with 92 protons and 235 nucleons (protons + neutrons) is undergoing nuclear decay and producing a helium nucleus (2 protons) along with another product.
To determine the missing product, we need to balance the number of protons and nucleons on both sides. Since the number of protons must remain the same, the total number of protons on the left side should be equal to the total number of protons on the right side.
On the left side, uranium has 92 protons. On the right side, helium also has 2 protons. Therefore, the missing product should have 90 protons.
Now we need to balance the number of nucleons. On the left side, uranium has 235 nucleons (protons + neutrons). On the right side, helium has 2 nucleons.
To calculate the number of neutrons in the missing product, we subtract the number of protons (90 protons) from the total number of nucleons (231 nucleons in this case since 231 comes from Pa-231 in the multiple-choice options).
The number of neutrons in the missing product = Total number of nucleons - Number of protons
= 231 nucleons - 90 protons
= 141 neutrons
So, the missing product in the nuclear equation is an isotope with 90 protons and 141 neutrons. Comparing the options, the correct answer is:
c) Th - 231