Page 505 - Physics Coursebook 2015 (A level)

Chapter 31: Nuclear physics
WORKED EXAMPLE
3 Use the data below to determine the minimum energy required to split a nucleus of oxygen-16 (168O) into its separate nucleons. Give your answer in joules (J).
mass of proton = 1.672 623 × 10−27 kg
mass of neutron = 1.674 929 × 10−27 kg
mass of 168O nucleus = 26.551 559 × 10−27 kg speedoflightc=3.00×108ms−1
Step1 FindthedifferenceΔminkgbetweenthe mass of the oxygen nucleus and the mass of the individual nucleons. The 168O nucleus has 8 protons and 8 neutrons.
Δm = final mass − initial mass
Δm = [(8 × 1.672 623 + 8 × 1.674 929) − 26.551 559]−27
×10 kg
Δm≈2.20×10−28kg
There is an increase in the mass of this system
because external energy is supplied.
Step2 UseEinstein’smass–energyequationto determine the energy supplied.
ΔE=Δmc2
E=2.20×10−28 ×(3.00×108)2 ≈1.98×10−11J
QUESTIONS
3 The Sun releases vast amounts of energy. Its power output is 4.0 × 1026 W. Estimate by how much its mass decreases each second because of this energy loss.
Another unit of mass
When calculating energy values using E = mc2, it is essential to use values of mass in kg, the SI unit of
mass. However, the mass of a nucleus is very small, perhaps 10−25 kg, and these numbers are awkward. As an alternative, atomic and nuclear masses are often given in a different unit, the atomic mass unit (symbol u).
It follows that the mass of an atom of 162C = 12.000u exactly. (An alternative might have been to define the mass of a proton as 1.000 u exactly, but it is more practical to measure the mass of an atom of the carbon isotope 126C.)
Table 31.3 shows the masses of some nuclides in u.
1uisdefinedas1 ofthemassofaneutralatomof
12 carbon-12.
Nuclide
Symbol
Mass/u
proton
neutron
helium-4
carbon-12
potassium-40
uranium-235
1 1p
01n
42He
162C
40 K 19
235 U 92
1.007 825
1.008 665
4.002 602
12.000 000
39.963 998
235.043 930
4 a
Calculate the energy released if a 42He nucleus is formed from separate protons and neutrons. The masses of the particles are given in
Table 31.2.
Table 31.3 Masses of some nuclides in atomic mass units. Some have been measured to several more decimal places than are shown here.
The atomic mass unit is related to the kilogram by: 1 u = 1.660 538 921(73) × 10−27 kg
This conversion factor is found by measuring the mass in kg of atoms of carbon-12. (The bracketed figures represent the experimental uncertainty.)
To convert a mass in u to kg, multiply by the conversion factor shown above (usually 1.6605 × 10−27 is sufficiently accurate).
From Table 31.3, you can see that the mass in u is close to the nucleon number A. For example, the mass of uranium-235 is slightly more than 235. The extra bit is known as the mass excess.
mass excess = mass (in u) – nucleon number
So the mass excess for U-235 is 235.043 930 − 235 = 0.043 930 u.
b Calculate also the energy released per nucleon.
Table 31.2 Masses of some particles.
5 A golf ball has a mass of 150 g. Calculate its increase in mass when it is travelling at 50 m s−1. What is this as a percentage of its rest mass?
Particle
Mass / 10−27 kg
1p
1.672 623
01n
1.674 929
42He
6.644 661
493