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1 Three isotopes of uranium have mass numbers of 234, 235, and 238 The atomic number of uranium is 92 How many neutrons are in the nuclei of each of these isotopes 2 An isotope of oxygen has a mass number of 15 How many neutrons are in the nucleus of this isotope 3 How many neutrons are in the mercury isotope 200Hg 80 4 Write the symbols for the three isotopes of hydrogen that have zero, one, and two neutrons in the nucleus

The negatively charged electrons that surround the positively charged nucleus of an atom are held in place by the attractive electromagnetic force Because the nucleus consists of positively charged protons and neutral neutrons, the repulsive electromagnetic force among the protons might be expected to cause them to fly apart Because this does not happen, an even stronger attractive force must exist within the nucleus

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The strong nuclear force, also called the strong force, acts between protons and neutrons that are close together, as they are in a nucleus This force is more than 100 times stronger than the electromagnetic force The range of the strong force is short, only about the radius of a proton, 14 10 15 m It is attractive and is of the same strength among protons and protons, protons and neutrons, and neutrons and neutrons Both neutrons and protons are called nucleons The strong nuclear force holds the nucleons in the nucleus If a nucleon were to be pulled out of a nucleus, work would have to be done to overcome the attractive force Doing work adds energy to the system Thus, the assembled nucleus has less energy than the separate protons and neutrons that make it up The difference is the binding energy of the nucleus Because the assembled nucleus has less energy, all binding energies are negative

Forces A positron is a positively charged electron The electromagnetic attraction of an electron and a positron is 42 1042 times stronger than their gravitational attraction

Einstein showed that mass and energy are equivalent, so the binding energy can be expressed in the form of an equivalent amount of mass, according to the following equation Energy Equivalent of Mass E mc2

C:\Program Files\PostgreSQL\82\bin>psql -q test fred Password for user fred: test=> select * from :cust; CustomerID | LastName | FirstName | Address | City | State | Zip | Phone + + + + + + + BLU001 | Blum | Rich | 123 Main | Chicago | IL | 60633 | 555-1234 (1 row) test=>

The energy contained in matter is equal to the mass times the square of the speed of light in a vacuum

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Because energy has to be added to take a nucleus apart, the mass of the assembled nucleus is less than the sum of the masses of the nucleons that compose it For example, the helium nucleus, 4He, consists of two protons and two 2 neutrons The mass of a proton is 1007276 u The mass of a neutron is 1008665 u If the mass of the helium nucleus were equal to the sum of the masses of the two protons and the two neutrons, you would expect that the mass of the nucleus would be 4031882 u Careful measurement, however, shows that the mass of a helium nucleus is only 4002603 u The actual mass of the helium nucleus is less than the mass of its constituent parts by 0029279 u The difference between the sum of the masses of the individual nucleons and the actual mass is called the mass defect Mass spectrometers usually measure the masses of isotopes; that is, the nuclides with all their electrons When calculating the mass defect of a nucleus, one must make sure that the mass of the electrons is accounted for properly Thus, the mass of hydrogen (one proton and one electron) usually is given in mass-defect problems

Masses normally are measured in atomic mass units It will be useful, then, to determine the energy equivalent of 1 u (16605 10 27 kg) To determine the energy, you must multiply the mass by the square of the speed of light in a vacuum (29979 108 m/s) This is expressed to five significant digits E mc2 (16605 10 27 kg)(29979 108 m/s)2 14924 10 10 kg m2/s2 14924 10 10 J

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