# 2.4: Neutrons: Isotopes and Mass Number Calculations (2023)

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Learning objectives
• Describe the location, charge, and relative mass of the neutron.
• Define isotope and mass number.
• Determine the number of protons, neutrons, and electrons in a specific isotope of an element.
• Represent a single isotope of an element using the three main elemental symbolisms.

The final subatomic particle was not discovered until 1932. To account for the neutral charge of an atom as a whole, the number of positively charged protons and negatively charged electrons found within an atom must be equal. Therefore, any remaining subatomic particles must be discharged so as not to disturb this established charge balance. In fact,neutrons, which received this name because of their neutral charge, have no electrical properties. Consequently, these subatomic particles, which are symbolized by the notation "n0", were incredibly difficult to detect. Neutrons are also found in the nucleus of an atom, and the mass of a neutron has been found to befairslightly greater than the mass of a proton.

Each subatomic particle exists to serve a specific purpose. As indicated in the previous section, the number of valence electrons present in an atom determines the reactivity of that element. The number of protons found within an atom defines that atom's identity, and all of an atom's protons collectively attract surrounding electrons, holding the latter attached to the atom. Remember, however, that all the protons, each with a +1 charge, are close together in the central region of an atom. Therefore, every positively charged proton must be strongly repelled by every other proton in the nucleus, and furthermore, the combined force of these repulsion forces is substantial enough to fragment the nucleus. However, neutrons effectively act as "nuclear glue" and allow protons to exist in physical proximity to one another. In other words, neutrons are the subatomic particle responsible for maintaining the structural integrity of the nucleus.

Finally, remember that each atom of a given element must have a definite number of protons and electrons. Every carbon atom, C, that exists in the known universe isdefinedit must contain 6 protons, because its atomic number is 6, and it must also contain 6 electrons, in order for the atom to maintain an overall neutral charge. However, the number of neutrons within an atom of an element isNodefined by the atomic number of that element. In fact, the number of neutrons present in an element can vary from one atom to another. The "glue" analogy found in the previous paragraph can be extended to explain this phenomenon. While a minimal amount of glue is required to adhere one object to another, a small amount of excess glue will not prevent these objects from sticking together, but a large amount of excess glue can be problematic. Likewise, each element must contain a minimum number of neutrons to hold the nucleus together, but can contain a small number of additional neutrons without sacrificing the structural integrity of the nucleus. However, a nucleus that contains too many neutrons will become unstable and sufferradioactive decay, which will be discussed in Chapter 9 of this text.

### mass number

Omass numberof an atom is equal to the total number of protons and neutrons contained in its nucleus. This definition can be represented in an equation, as shown below.

Mass number = # of protons + # of neutrons

The true mass of an atom is an incredibly small amount. To simplify the numerical values ​​used, the mass of a single proton is given the value of 1atomic mass unit, oamor. Since the mass of a neutron is about the same as the mass of a proton, each neutron present is also assigned a value of 1 amu. Since the mass of an electron is 1/2000ºOf the mass of a proton, any contribution that electrons make to the total mass of an atom is negligible. Therefore, the number of electrons present in an atom is ignored when calculating the mass number of that atom.

Example $$\PageIndex{1}$$

use aperiodic tableto calculate the mass number of a hydrogen atom that contains 2 neutrons.

Solution

The mass number of an atom is calculated by adding the number of protons and neutrons found within that atom. The number of neutrons is given, but the number of protons must be determined from the atomic number of the element. In this case, hydrogen (H) has atomic number 1, so each hydrogen atom will contain 1 proton. The equation shown above can be applied as follows.

Mass number = # of protons + # of neutrons
Mass number = 1 + 2

So this particular hydrogen atom will have a mass number of3.

Note that the mass number calculated in Example $$\PageIndex{1}$$ does not match the number under the elemental symbol and name for hydrogen on the periodic table. This discrepancy can be explained by a subtle but incredibly important piece of information: The calculation performed on Example $$\PageIndex{1}$$ was done tosingle atomof hydrogen. However, the periodic table purports to representallhydrogen atoms in the known universe. Fromallexisting hydrogen atom must contain 1 proton, the atomic number that is written above the elemental symbol for hydrogen actually representsallhydrogen atom.

However, remember that the number of neutrons contained in an element can vary from one atom to another. Changing the number of neutrons present in an atom will, in turn, cause those individual hydrogen atoms to have different calculated mass numbers. These individual "versions" of an element are calledisotopes, which are defined as atoms of an element that have the same atomic number and therefore contain the same number of protons but different mass numbers and therefore contain a different number of neutrons. Figure $$\PageIndex{1}$$ models three isotopes of hydrogen. Most hydrogen atoms have one proton, one electron, and contain no neutrons, but less common isotopes of hydrogen may contain one or two neutrons. Hydrogen is unique in that its isotopes are given special names, which are also shown below in Figure $$\PageIndex{1}$$.

For spatial reasons, it is not practical to list the mass numbers of all the isotopes of an element within a single box on the periodic table. Instead, a weighted average, calledaverage atomic mass, is calculated. A weighted average takes into account not only the mass number of each isotope, but also how frequent or common that isotope is in nature, relative to each of the other isotopes of that element. Therefore, an average atomic mass is a quantity that actually representsallisotopes of a given element, making it suitable for inclusion in the periodic table.

Example $$\PageIndex{2}$$

use aperiodic tableto determine the following information for an atom that has an atomic number of 74 and a mass number of 186.

1. elemental symbol
2. elemental name
3. Number of protons contained in the atom.
4. Number of electrons contained in the atom.
5. Number of neutrons contained in the atom.

Solutions

1. The atomic number of an element is located above the element symbol within a box on the periodic table. The element with an atomic number of 74 is symbolized asC.
2. The element with an atomic number of 74 is calledtungsten.
3. The number of protons present in an atom is defined by the atomic number of the element. Therefore, each tungsten atom contains74 protons.
4. Since an atom must have an overall neutral charge, the number of protons and electrons found within an atom of an element must be equal. Therefore, each tungsten atom also contains74 electrons.
5. The mass number of an atom is calculated by adding the number of protons and neutrons found within that atom, as shown below.

Mass number = # of protons + # of neutrons

Since the mass number was given, this equation can be rearranged to determine the number of neutrons contained in this particular isotope of tungsten.

186 = 74 + # of neutrons
186 - 74 = # of neutrons

Therefore, this particular tungsten atom contains112 neutrons.

### elemental symbolisms

In total, 252 stable isotopes of 80 different elements have been isolated. Taking into account the number of unstable isotopes that have been observed, the total number of known elemental isotopes increases substantially. Although each of the three most common isotopes of hydrogen has a unique name, it would be highly impractical to give them different names.allisotope ofallelement that has been shown to exist. Therefore, scientists use threeelemental symbolismsto refer to specific elemental isotopes. The first two symbolisms are very similar in that each includes the elemental name, or elemental symbol, of an element, followed by a hyphen and a numerical value, which corresponds to the mass number of a particular isotope of that element. In the third type of elemental symbolism, callednuclear symbol, the isotope's mass number is placed as a superscript before an element's symbol, and the element's atomic number is written directly below the mass number. It is important to note the difference between aisotopeit's aelemental symbolism. The figure $$\PageIndex{2}$$ models these threedifferent elemental symbolisms, which represent allsameisotopebecause each one has aidenticalmass number

Example $$\PageIndex{3}$$

Write the nuclear symbol of the isotope described in Example $$\PageIndex{2}$$.

Solutions
In a nuclear symbol, the isotope's mass number is placed as a superscript before an element's symbol, and the element's atomic number is written directly below the mass number.

The example isotope $$\PageIndex{2}$$ has an atomic number of 74, a mass number of 186, and is symbolized as W. When this information is incorporated into this notation, the nuclear symbol shown below is obtained. continuation.

$$\ce{^{186}_{74}W}$$

Example $$\PageIndex{4}$$

Determine how many protons, electrons, and neutrons are present in an atom of each of the following isotopes.

1. $$^{40}_{19}\ce{K}$$
2. Five-65

Solutions

1. This isotope is symbolized by a nuclear symbol. In this notation, the atomic number of the isotope is written as a subscript. Since the atomic number indicates both the number of protons and the number of electrons present in an atom, this isotope contains19 protonsmi19 electrons. The number of neutrons in the isotope can be calculated from its mass number, which is written as a superscript in a nuclear symbol.

Mass number = # of protons + # of neutrons
40 = 19 + # of neutrons
40 - 19 = # of neutrons

then there is21 neutronsin this isotope of potassium (K).

2. This isotope is represented using the second symbolism shown in Figure $$\PageIndex{2}$$. When using this notation, the name of the element must be used to find its atomic number. Since zinc (Zn) has an atomic number of 30, this isotope contains30 protonsmi30 electrons. The number of neutrons in the isotope can be calculated again from its mass number, which is the numerical value written after the hyphen in both representations shown in Figure $$\PageIndex{2}$$.

Mass number = # of protons + # of neutrons
65 = 30+ # of neutrons
65 - 30 = # of neutrons

then there is35 neutronsin this zinc isotope (Zn).

Exercise $$\PageIndex{1}$$

Determine how many protons, electrons, and neutrons are present in an atom of each of the following isotopes.

1. $$^{60}_{27}\ce{Co}$$
2. uranium-238
3. of the 25th
Responder a
This isotope is represented by a nuclear symbol. In this notation, the atomic number of the isotope is written as a subscript. Since the atomic number indicates both the number of protons and the number of electrons present in an atom, this isotope contains27 protonsmi27 electrons. The number of neutrons in the isotope can be calculated from its mass number, which is written as a superscript in a nuclear symbol.

Mass number = # of protons + # of neutrons
60 = 27 + # of neutrons
60 - 27 = # of neutrons

then there is33 neutronsin this isotope of cobalt (Co).
This isotope is represented using the second symbolism shown in Figure $$\PageIndex{2}$$. When using this notation, the name of the element must be used to find its atomic number. Since uranium (U) has an atomic number of 92, this isotope contains92 protonsmi92 electrons. The number of neutrons in the isotope can again be calculated from its mass number, which is the numerical value written after the hyphen in both representations shown in Figure $$\PageIndex{2}$$.

Mass number = # of protons + # of neutrons
238 = 92 + # of neutrons
238 - 92 = # of neutrons

then there is146 neutronsin this uranium (U) isotope.
This isotope is represented using the first symbolism shown in Figure $$\PageIndex{2}$$. When using this notation, the element's symbol must be used to find its atomic number. Since sodium (Na) has atomic number 11, this isotope contains11 protonsmi11 electrons. The number of neutrons in the isotope can again be calculated from its mass number, which is the numerical value written after the hyphen in both representations shown in Figure $$\PageIndex{2}$$.

Mass number = # of protons + # of neutrons
25 = 11 + # of neutrons
25 - 11 = # of neutrons

then there is14 neutronsin this isotope of sodium (Na).

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