How To Find The Number Of Neutrons In An Isotope

2.4: Neutrons: Isotopes and Mass Number Calculations

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Learning Objectives

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

The final subatomic particle was not discovered until 1932.  In order to business relationship for the neutral charge of an cantlet equally a whole, the number of positively-charged protons and negatively-charged electrons found within an atom must be equal.  Therefore, whatsoever remaining subatomic particles must be uncharged, so as to not upset this established accuse balance.  Indeed, neutrons, which were named as a outcome of their neutral charge, do not possess any electrical properties.  Consequently, these subatomic particles, which are symbolized using the notation "n⁰," were incredibly difficult to detect.  Neutrons are too located in the nucleus of an atom, and the mass of a neutron was institute to bejustslightly greater than the mass of a proton.

Each subatomic particle exists to serve a specific purpose.  As stated in the previous section, the number of valence electrons nowadays in an atom dictates the reactivity of that element.  The number of protons constitute within an atom defines the identity of that cantlet, and all of an atom's protons collectively concenter the surrounding electrons, keeping the latter bound to the atom.  Recall, nevertheless, that all protons, which each deport a +i charge, are densely-packed into the fundamental region of an atom.  Therefore, each positively-charged proton must exist strongly repelled by every other proton in the nucleus, and, furthermore, the combined force of these repulsive forces is substantial enough to splinter the nucleus.  All the same, neutrons effectively act every bit "nuclear mucilage" and let the protons to be in close physical proximity to one another.  In other words, neutrons are the subatomic particle responsible for maintaining the structural integrity of the nucleus.

Finally, recall that every atom of a sure chemical element must take a defined number of protons and electrons.  Every atom of carbon, C, that exists in the known universe isdefined to contain 6 protons, because its atomic number is 6, and must also contain six electrons, in club for the atom to maintain an overall internet neutral charge.  Even so, the number of neutrons inside an atom of an element is not defined by the atomic number of that element.  In fact, the number of neutrons present in an element tin vary from atom to atom.  The "glue" analogy found inside the previous paragraph tin can be extended to explain this phenomenon.  While a minimum amount of glue is required to adhere ane object to another, a small amount of excess glue will not foreclose those objects from sticking together, just a large excess of glue could bear witness to be problematic.  Likewise, each chemical element must contain a minimum number of neutrons to hold the nucleus together, but could contain a small number of additional neutrons without sacrificing the structural integrity of the nucleus.  Notwithstanding, a nucleus that contains too many neutrons volition become unstable and undergoradioactive decay, which will be discussed in Chapter ix of this text.

Mass Number

The mass number of an cantlet is equal to the full 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 minor quantity.  To simplify the numerical values being used, the mass of a unmarried proton is assigned a value of 1 atomic mass unit of measurement, or amu.  Equally the mass of a neutron is approximately the same as the mass of a proton, each neutron that is present is as well given a value of 1 amu.  Since the mass of an electron is one/ii,000^th of the mass of a proton, any contribution that electrons make to the overall mass of an atom is negligible.  Therefore, the number of electrons present in an atom are ignored when calculating the mass number of that atom.

Example \(\PageIndex{1}\)

Utilize a periodic tabular array to calculate the mass number of a hydrogen atom that contains ii neutrons.

Solution

The mass number of an atom is calculated by calculation together the number of protons and neutrons that are establish inside that atom. The number of neutrons is given, but the number of protons must be determined from the atomic number for the element. In this case, hydrogen (H) has an atomic number of 1 and, therefore, every atom of hydrogen volition incorporate one proton. The equation shown above can then exist practical, every bit follows.

Mass Number = # of Protons + # of Neutrons
Mass Number = 1 + 2

Therefore, this particular cantlet of hydrogen will have a mass number of three.

Note that the mass number calculated in Example \(\PageIndex{one}\) does not match the number underneath the elemental symbol and proper noun for hydrogen on the periodic table.  This discrepancy can be explained by a subtle, only incredibly of import, piece of information:  The calculation performed in Example \(\PageIndex{one}\) was done for asingle atom of hydrogen.  Nevertheless, the periodic tabular array is intended to representall of the atoms of hydrogen in the known universe.  Sinceevery existing atom of hydrogen must contain 1 proton, the atomic number that is written in a higher place hydrogen's elemental symbol truly does representevery atom of hydrogen.

However, recall that the number of neutrons contained in an element can vary from cantlet to atom.  Changing the number of neutrons present in an atom will, in turn, cause these private atoms of hydrogen to take different calculated mass numbers.  These individual "versions" of an element are called isotopes, which are divers as atoms of an element that have the same atomic numbers and, therefore, contain the same number of protons, simply different mass numbers, and, therefore, contain differing numbers of neutrons. 3 isotopes of hydrogen are modeled in Effigy \(\PageIndex{1}\). Most hydrogen atoms take i proton, i electron, and do not contain whatever neutrons, but less common isotopes of hydrogen can contain either i or two neutrons.  Hydrogen is unique, in that its isotopes are given special names, which are as well shown beneath in Figure \(\PageIndex{one}\).

Figure \(\PageIndex{1}\): The 3 most stable isotopes of hydrogen.

For spatial reasons, listing the mass numbers for all of an element's isotopes within a single box on the periodic table is impractical.  Instead, a weighted average, called anatomic mass average, is calculated.  A weighted average takes into business relationship non merely the mass number of each isotope, just as well how prevalent, or mutual, that isotope is in nature, relative to each of that element'south other isotopes.  Therefore, an atomic mass boilerplate is a quantity that truly represents all isotopes of a given element, making it appropriate for inclusion on the periodic table.

Case \(\PageIndex{2}\)

Utilise a periodic table to determine the post-obit 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 found above the elemental symbol within a box on the periodic table.  The element with an atomic number of 74 is symbolized as W.
2. The chemical element with an diminutive number of 74 is named tungsten.
3. The number of protons present in an atom is defined by the element'south atomic number.  Therefore, every atom of tungsten contains74 protons.
4. Since an atom must take an overall neutral charge, the number of protons and electrons constitute inside an atom of an chemical element must be equal.  Therefore, every atom of tungsten too contains74 electrons.
5. The mass number of an atom is calculated by adding together the number of protons and neutrons that are establish within that cantlet, as shown below.

   Mass Number = # of Protons + # of Neutrons

   Since the mass number was provided, this equation can be rearranged to make up one's mind the number of neutrons contained in this specific isotope of tungsten.

   186 = 74 + # of Neutrons
   186 - 74 = # of Neutrons

   Therefore, this particular cantlet of tungsten contains 112 neutrons.

Elemental Symbolisms

In total, 252 stable isotopes have been isolated for fourscore different elements.  Factoring in the number of unstable isotopes that have been observed causes the total number of known elemental isotopes to increment substantially.  While each of hydrogen'southward iii nearly common isotopes has a unique proper name, it would ultimately exist highly impractical to establish different names forevery isotope ofevery element that has been shown to be.  Therefore, scientists apply three dissimilar elemental symbolisms to refer to specific elemental isotopes.  The offset two symbolisms are very like, in that each includes the elemental name, or elemental symbol, of an element, followed by a nuance and a numerical value, which corresponds to the mass number of a particular isotope of that element.  In the third type of elemental symbolism, which is called anuclear symbol, the mass number of the isotope is positioned as a superscript before an elemental symbol, and the atomic number of the element is written directly underneath the mass number.  It is important to notation the difference between an isotope and an elemental symbolism.  Figure \(\PageIndex{two}\) models these threeunlike elemental symbolisms , which all represent thesame isotope , since each has an identical mass number.

Figure \(\PageIndex{2}\):  Three elemental symbolisms for a single isotope of nickel.

Example \(\PageIndex{3}\)

Write the nuclear symbol of the isotope that is described in Example \(\PageIndex{2}\).

Solutions
In a nuclear symbol, the mass number of the isotope is positioned as a superscript before an elemental symbol, and the diminutive number of the element is written direct underneath the mass number.

The isotope in Example \(\PageIndex{2}\) has an atomic number of 74, a mass number of 186, and is symbolized every bit W.  When this data is incorporated into this notation, the nuclear symbol shown below results.

\(\ce{^{186}_{74}W}\)

Example \(\PageIndex{iv}\)

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

1. \(^{40}_{nineteen}\ce{K}\)
2. Zinc-65

Solutions

1. This isotope is symbolized using a nuclear symbol.  In this notation, the atomic number of the isotope is written equally a subscript.  Since the diminutive number indicates both the number of protons and the number of electrons present in an atom, this isotope contains 19 protons and 19 electrons.  The number of neutrons in the isotope can be calculated from its mass number, which is written equally a superscript in a nuclear symbol.

   Mass Number = # of Protons + # of Neutrons
   40 = nineteen + # of Neutrons
   40 - 19 = # of Neutrons

   Therefore, there are 21 neutrons in this isotope of potassium (G).

2. This isotope is represented using the second symbolism shown in Effigy \(\PageIndex{2}\).  When using this notation, the name of the chemical element must be used to notice its atomic number.  Since zinc (Zn) has an atomic number of 30, this isotope contains 30 protons and 30 electrons.  The number of neutrons in the isotope tin again be calculated from its mass number, which is the numerical value written after the nuance in both representations shown in Figure \(\PageIndex{two}\).

   Mass Number = # of Protons + # of Neutrons
   65 = xxx + # of Neutrons
   65 - 30 = # of Neutrons

   Therefore, there are 35 neutrons in this isotope of zinc (Zn).

Exercise \(\PageIndex{1}\)

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

1. \(^{60}_{27}\ce{Co}\)
2. Uranium-238
3. Na-25

Answer a

This isotope is represented using a nuclear symbol.  In this notation, the atomic number of the isotope is written every bit a subscript.  Since the atomic number indicates both the number of protons and the number of electrons nowadays in an cantlet, this isotope contains 27 protons and 27 electrons.  The number of neutrons in the isotope tin be calculated from its mass number, which is written equally a superscript in a nuclear symbol.

Mass Number = # of Protons + # of Neutrons
sixty = 27 + # of Neutrons
lx - 27 = # of Neutrons

Therefore, there are 33 neutrons in this isotope of cobalt (Co).

Answer b

This isotope is represented using the second symbolism shown in Figure \(\PageIndex{2}\).  When using this note, the proper noun of the chemical element must be used to detect its atomic number.  Since uranium (U) has an diminutive number of 92, this isotope contains 92 protons and 92 electrons.  The number of neutrons in the isotope can over again be calculated from its mass number, which is the numerical value written subsequently the dash in both representations shown in Figure \(\PageIndex{2}\).

Mass Number = # of Protons + # of Neutrons
238 = 92 + # of Neutrons
238 - 92 = # of Neutrons

Therefore, there are 146 neutrons in this isotope of uranium (U).

Answer c

This isotope is represented using the starting time symbolism shown in Figure \(\PageIndex{ii}\).  When using this notation, the symbol of the chemical element must be used to discover its atomic number.  Since sodium (Na) has an atomic number of 11, this isotope contains 11 protons and 11 electrons.  The number of neutrons in the isotope can once again be calculated from its mass number, which is the numerical value written after the dash in both representations shown in Figure \(\PageIndex{2}\).

Mass Number = # of Protons + # of Neutrons
25 = xi + # of Neutrons
25 - xi = # of Neutrons

Therefore, there are 14 neutrons in this isotope of sodium (Na).

Source: https://chem.libretexts.org/Courses/Heartland_Community_College/CHEM_120:_Fundamentals_of_Chemistry/02:_Atoms_and_Elements/2.04:_Neutrons:__Elemental_Isotopes_and_Mass_Number_Calculations

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