Question 1

Nuclear binding energy: Uranium-238 decays into thorium-234 plus an alpha particle. How much energy is released in this process? 1 u = 931.494 MeV/c², and the relevant mass values are He: 4.002603 u Th: 234.043583 u U: 238.050786 u

Accepted Answer

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Question 2

Nuclear fusion: A fusion reaction releases energy because the binding energy of the resulting nucleus

Accepted Answer

In a fusion reaction, two or more atomic nuclei come together to form a heavier nucleus. This process releases energy because the binding energy of the resulting nucleus is greater than the sum of the binding energies of the original nuclei. This excess binding energy is released in the form of kinetic energy of particles and radiation. Therefore, choice A is the correct answer.

Question 3

Nuclear fusion: The primary source of the energy radiated by a star, such as the sun, is

Accepted Answer

The primary source of the energy radiated by a star, such as the sun, is fusion reactions in which hydrogen is fused to form helium. Nuclear fusion is the process of combining atomic nuclei to form a heavier nucleus, releasing energy in the process. In the sun, hydrogen atoms are fused under high temperatures and pressures to form helium atoms, releasing a tremendous amount of energy in the form of light and heat.

Question 4

Nuclear binding energy: The neutral deuterium atom, H, has a mass of 2.014102 u; a neutral hydrogen atom has a mass of 1.007825 u; a neutron has a mass of 1.008665 u; and a proton has a mass of 1.007277 u. What is the binding energy of the H nucleus? (1 u = 931.494 MeV/c²)

Accepted Answer

We can calculate the mass defect of the 11eb6b7b_2f34_a207_b0cf_dd20e9618c41_TB8274_11 H nucleus as follows:

Mass of protons = 2 × 1.007277 u = 2.014554 u
Mass of neutrons = 1 × 1.008665 u = 1.008665 u
Mass of 11eb6b7b_2f34_a207_b0cf_dd20e9618c41_TB8274_11 H nucleus = 2.014102 u

Mass defect = (2.014554 + 1.008665) - 2.014102 = 0.008117 u

The binding energy can be calculated using Einstein's famous equation, E=mc²:

Binding energy = 0.008117 u × 931.494 MeV/c² = 7.565 MeV

Therefore, the binding energy of the 11eb6b7b_2f34_a207_b0cf_dd20e9618c41_TB8274_11 H nucleus is 7.565 MeV. However, we are asked for the binding energy per nucleon, so we divide by the number of nucleons in the nucleus:

Binding energy per nucleon = 7.565 MeV / 2 = 3.7825 MeV

Therefore, the best choice is C, 2.2 MeV, because it is the closest choice to 3.7825 MeV.

Question 5

Nuclear binding energy: The carbon in your body was formed in nuclear reactions in long-dead stars. How much energy was released when three ⁴He nuclei combined to make ¹²C? The mass of ⁴He is 4.002603 u, the mass of ¹²C is 12.0000 u, and 1 u = 931.494 MeV/c².

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Question 6

Nuclear binding energy: The set of nuclear reactions that power our sun can be summarized a 4p⁺ → ⁴He⁺² + 2e⁺. The masses of the particles involved are 938.272 MeV/c² (proton, p⁺), 3727.38 MeV/c² (alpha particle, ⁴He⁺²), and 0.511 MeV/c² (positron, e⁺). How much energy is released by each set of these reactions?

Accepted Answer

The energy released is calculated by taking the mass difference before and after the reaction and converting it to energy using Einstein's equation E=mc^2. Before the reaction, the total mass is 4 protons * 938.272 MeV/c^2 = 3753.088 MeV/c^2. After the reaction, the total mass is the mass of the alpha particle (3727.38 MeV/c^2) plus 2 positrons (2 * 0.511 MeV/c^2 = 1.022 MeV/c^2), totaling 3728.402 MeV/c^2. The mass difference is 3753.088 - 3728.402 = 24.686 MeV/c^2, which is approximately 24.69 MeV, indicating the energy released by the reaction.

Question 7

Nuclear binding energy: A stationary plutonium-239 nucleus decays into a uranium-235 nucleus plus an alpha particle. The energy released in the process is 5.24 MeV. Given the following mass values He: 4.002603 u U: 235.043924 u what is the kinetic energy of the U nucleus? (1 u =931.494 MeV/c²)

Accepted Answer

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Question 8

Nuclear fusion: How does the mass of the products of a nuclear fusion reaction compare to the mass of the original elements?

Accepted Answer

In a nuclear fusion reaction, the mass of the products is less than the mass of the original elements because a small amount of mass is converted into energy according to Einstein's famous equation E=mc². This energy is released in the form of gamma rays, which carries away some of the original mass. This phenomenon is known as mass-energy equivalence. Therefore, the total mass of the products is less than the total mass of the original elements.

Question 9

Properties of the nucleus: A certain nucleus containing 8 protons and 7 neutrons has a density ρ. Which of the following values would be closest to the expected value of the density of a nucleus having 51 protons and 69 neutrons?

Accepted Answer

The density of a nucleus is approximately constant across different nuclei because it depends on the volume and mass of the nucleus, both of which scale with the number of nucleons (protons and neutrons). Since the volume and mass increase proportionally with the number of nucleons, the density remains roughly the same.

Question 10

Nuclear binding energy: The following masses are known: n (neutron) 1.008665 u H 1.007825 u Fe 56.935399 u What is the binding energy of Fe, in MeV? (1 u = 1.6605 × 10^-27 kg = 931.5 MeV/c²)

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Question 11

Nuclear binding energy: Radium-226 decays into radon-222 plus an alpha particle. How much energy is released in this process? 1 u = 931.494 MeV/c2, and the relevant mass values are  He: 4.002603 u  Rn: 222.017570 u  Ra: 226.025402 u

Accepted Answer

The total mass before the decay is: 
226.025402 u 
The total mass after the decay is: 
222.017570 u (for Rn) + 4.002603 u (for He) = 226.020173 u 
The difference in mass is: 
226.025402 u - 226.020173 u = 0.005229 u

Converting to energy using 1 u = 931.494 MeV/c^2:

0.005229 u × 931.494 MeV/c^2 = 4.87 MeV

Therefore, the answer is C.

Question 12

Properties of the nucleus: What would be the expected radius of a nucleus having 82 protons and 125 neutrons?

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Question 13

Nuclear fusion: In massive stars, three helium nuclei fuse together, forming a carbon nucleus. This reaction heats the core of the star. The net mass of the three helium nuclei must therefore be

Accepted Answer

The net mass of the three helium nuclei is higher than that of the carbon nucleus because some of the mass is converted into energy according to Einstein's equation E=mc^2. This mass difference is what releases energy during the fusion process, heating the core of the star.

Question 14

Nuclear binding energy: What is the binding energy per nucleon for Al? The neutral Al atom has a mass of 26.981539 u; a neutral hydrogen atom has a mass of 1.007825 u; a neutron has a mass of 1.008665 u; and a proton has a mass of 1.007277 u. (1 u = 931.494 MeV/c²)

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Question 15

Properties of the nucleus: If a nucleus had a diameter of 8.0 fm, what would be its expected mass, in atomic mass units?

Accepted Answer

The mass of a nucleus can be estimated using its diameter and the fact that the nuclear density is approximately constant. The formula relating the mass number (A) to the radius (R) of a nucleus is $R = R_0 A^{1/3}$, where $R_0$ is a constant approximately equal to 1.2 fm. Rearranging this formula to solve for A gives $A = \left(\frac{R}{R_0}\right)^3$. Substituting $R = 8.0$ fm and $R_0 = 1.2$ fm gives $A = \left(\frac{8.0}{1.2}\right)^3 \approx 296$, which means the expected mass is about 296 atomic mass units (u).

Question 16

Properties of the nucleus: What would be the expected radius of the nucleus of  Sr?

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Question 17

Properties of the nucleus: Two identical nuclei of mass 18 u are made to unite to make a single nucleus of mass 36 u. What is the radius of the result of this fusion?

Accepted Answer

The radius of a nucleus is proportional to the cube root of its mass number. Therefore, the radius of the resulting nucleus is 36^(1/3) = 4 fm.

Question 18

Nuclear binding energy: Plutonium-239 decays into uranium-235 plus an alpha particle. The energy released in the process is 5.24 MeV. Given the following mass values He: 4.002603 u U: 235.043924 u what is the mass of Pu in atomic mass units? (1 u = 931.494 MeV/c²)

Accepted Answer

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Question 19

Properties of the nucleus: A certain nucleus containing 8 protons and 7 neutrons has a radius R. Which of the following values would be closest to the expected value of the radius of a nucleus having 51 protons and 69 neutrons?

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Question 20

Nuclear binding energy: How much energy is released when 1.40 μg of ³H have decayed to ³He? The mass of ³He is 3.016029 u, the mass of ³H is 3.016049 u, and 1 u = 931.494 MeV/c².

Accepted Answer

The correct answer is A.The mass difference between ³H and ³He is 3.016049 u - 3.016029 u = 0.000020 u. The energy released is 0.000020 u * 931.494 MeV/c² = 830 J.

Quiz 34: Geometric Optics

Nuclear binding energy: Uranium-238 decays into thorium-234 plus an alpha particle. How much energy is released in this process? 1 u = 931.494 MeV/c2, and the relevant mass values are He: 4.002603 u Th: 234.043583 u U: 238.050786 u

Nuclear fusion: A fusion reaction releases energy because the binding energy of the resulting nucleus

Nuclear fusion: The primary source of the energy radiated by a star, such as the sun, is

Nuclear binding energy: The neutral deuterium atom, H, has a mass of 2.014102 u; a neutral hydrogen atom has a mass of 1.007825 u; a neutron has a mass of 1.008665 u; and a proton has a mass of 1.007277 u. What is the binding energy of the H nucleus? (1 u = 931.494 MeV/c2)

Nuclear binding energy: The carbon in your body was formed in nuclear reactions in long-dead stars. How much energy was released when three 4He nuclei combined to make 12C? The mass of 4He is 4.002603 u, the mass of 12C is 12.0000 u, and 1 u = 931.494 MeV/c2.

Nuclear binding energy: A stationary plutonium-239 nucleus decays into a uranium-235 nucleus plus an alpha particle. The energy released in the process is 5.24 MeV. Given the following mass values He: 4.002603 u U: 235.043924 u what is the kinetic energy of the U nucleus? (1 u =931.494 MeV/c2)