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In this lesson, we will learn how to relate the mass of a nucleus to the masses of its constituent particles and the binding energy of the nucleus.

Q1:

A supernova explosion of a 2 . 0 0 × 1 0 3 1 kg star produces 1 . 0 0 × 1 0 4 4 J of energy.

How many kilograms of mass are converted to energy in the explosion?

What is the ratio Δ 𝑚 / 𝑚 of mass destroyed to the original mass of the star?

Q2:

Protons have a rest energy of 938.28 MeV, neutrons have a rest energy of 939.57 MeV, and electrons have a rest energy of 511 keV. Six hydrogen atoms and six neutrons are combined to form an atom of 1 2 6 C . How much energy does this combination release if a unified atomic mass unit is equivalent to 931.494 MeV?

Q3:

For the reaction, n + H e H e + . 3 2 4 2 𝛾 Assume that the reactants are initially at rest.

Find the amount of energy transferred to the 4 2 H e .

Find the amount of energy transferred to the gamma-ray.

Q4:

Calculate the binding energy per nucleon of 5 6 2 6 F e . Use a value of 55.9349 u for the atomic mass of 5 6 2 6 F e . Use a value of 1.0073 u for the rest mass of a proton, 1.0087 u for the rest mass of a neutron, and 0.00055 u for the rest mass of an electron.

Q5:

The electrical power output of a large nuclear reactor facility is 900 MW. It has a 3 5 . 0 % efficiency in converting heat released by nuclear reactions to electrical energy.

What is the thermal power output?

How many 2 3 5 U nuclei undergo fission each second, assuming that the average energy released per fission is 200 MeV?

What mass of 2 3 5 U is fissioned in 1 year of full-power operation?

Q6:

The power output of the Sun is 4 × 1 0 2 6 W. 9 0 % of the Sun’s energy output is supplied by proton-proton chain reactions.

If a proton-proton chain reaction produces 26.7 MeV from the fusion of four protons into a helium nucleus, how many protons are consumed per second?

If a proton-proton chain reaction produces two neutrinos, how many neutrinos per second should there be per square meter at the surface of Earth from this process?

Q7:

The reactions of the proton-proton chain are 1 1 1 1 2 1 0 1 𝑒 H H H + → + 𝑒 + 𝜈 , 1 1 2 1 3 2 H H H e + → + 𝛾 , and 3 2 3 2 4 2 1 1 1 1 H e H e H H H + → + + . These reactions can be summarised as 4 → + 2 𝑒 + 2 𝛾 + 2 𝜈 1 1 4 2 0 1 𝑒 H H e . Use a value of 1.007825 for the atomic mass of 1 1 H , use a value of 4.002603 u for the atomic mass of 4 2 H , and use a value of 0.000549 u for the atomic mass of an electron. The gamma-ray photons produced in the reaction each have an energy of 0.511 MeV and the energy of the electron neutrino is negligible. How much energy is released in these reactions?

Q8:

A nuclear power plant converts energy from nuclear fission into electricity with an efficiency of 3 5 . 0 % . How much mass is destroyed in one year to produce a continuous 1 0 0 0 MW of electric power?

Q9:

The mass of subatomic particles contribute to the binding energy of nuclei. In determining the difference in binding energy between different nuclei, use a value of 1.0073 for the rest mass of a proton, 1.0087 u for the rest mass of a neutron, and 0.00055 for the rest mass of an electron.

Using a value of 235.0493 u for the atomic mass of 2 3 5 9 2 U , find its binding energy per nucleon.

Using a value of 238.0508 u for the atomic mass of 2 3 8 9 2 U , find its binding energy per nucleon.

Q10:

Calculate the energy released in the neutron induced fission reaction Use a value of 238.050788 u for the atomic mass of 2 3 8 9 2 U , use a value of 95.921750 u for the atomic mass of 9 6 3 8 S r , use a value of 139.92164 u for the atomic mass of 1 4 0 5 4 X e , and use a value of 1.0087 u for the rest mass of a neutron.

Q11:

A 1.00-kg mass mixture of deuterium and tritium fuses to produce helium. There are equal numbers of deuterium and tritium nuclei in the mixture. The energy released by the reaction depends on the mass differences between deuterium, tritium, and neutrons and can be calculated using a value of 2.014102 u for the atomic mass of deuterium, 3.016049 u for the atomic mass of tritium, 4.002603 u for the atomic mass of helium, and 1.008701 u for the atomic mass of neutrons.

How much energy is released by the fusion of the entire mixture?

If the reaction takes place continuously over exactly one year, what is the average power output from the reaction during that time?

Q12:

The sun produces energy at a rate of 3 . 8 5 × 1 0 2 6 W by the fusion of hydrogen. About 0 . 7 % of each kilogram of hydrogen goes into the energy generated by the Sun.

How many kilograms of hydrogen undergo fusion each second?

If the sun is 9 0 . 0 % hydrogen and half of this can undergo fusion before the sun changes character, how long could it produce energy at its current rate?

How many kilograms of mass is the sun losing per second?

What fraction of the Sun’s mass will it have lost after the Sun has fused half of its hydrogen?

Q13:

A person accidentally touches a 220 V AC power source and draws a current from it.

What current is drawn if the person is standing on a rubber mat that has a total resistance of 420 kΩ?

What current is drawn if the person is standing on wet grass that has a total resistance of 2 0 0 0 Ω?

Q14:

Seawater can be used in nuclear fusion reactions. The total energy available for fusion from the world’s seawater can be assumed to be 2 . 5 × 1 0 3 3 J, taking a value of 1 0 2 7 kg/m^{3} for the density of seawater.

What would be the decrease in mass of the world’s seawater?

What would be the decrease in the volume of the world’s seawater?

Q15:

Suppose an average home requires 600 kWh of electrical energy per month, and this power is produced by the destruction of a 0.90 g mass of matter converted to electrical energy with an efficiency of 48.0%.

For how long would the mass destroyed supply the required power?

How many homes could be supplied for one year by the energy from the mass conversion?

Q16:

Find the energy emitted in the 𝛽 − decay of Co-60, given that the atomic mass of Co-60 is 59.933819 u and that of Ni-60 is 59.930788 u. Give your answer to 4 significant figures.

Q17:

Calculate the mass equivalent in unified atomic mass units of the 13.6 eV binding energy of an electron in a hydrogen atom.

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