how to find the atomic mass of an isotope

Average Atomic Mass

The average atomic mass of an chemical element is the sum of the masses of its isotopes, each multiplied by its natural abundance.

Learning Objectives

Calculate the average atomic mass of an element given its isotopes and their natural abundance

Key Takeaways

Key Points

• An element can accept differing numbers of neutrons in its nucleus, but it e'er has the same number of protons. The versions of an element with dissimilar neutrons have unlike masses and are called isotopes.
• The average atomic mass for an element is calculated by summing the masses of the chemical element'southward isotopes, each multiplied by its natural abundance on Earth.
• When doing any mass calculations involving elements or compounds, ever apply average diminutive mass, which tin can be establish on the periodic table.

Key Terms

• mass number: The total number of protons and neutrons in an atomic nucleus.
• natural abundance: The abundance of a particular isotope naturally found on the planet.
• average diminutive mass: The mass calculated by summing the masses of an element'southward isotopes, each multiplied by its natural abundance on Globe.

The diminutive number of an chemical element defines the chemical element'southward identity and signifies the number of protons in the nucleus of one atom. For example, the element hydrogen (the lightest element) will ever have one proton in its nucleus. The element helium will always have two protons in its nucleus.

Isotopes

Atoms of the aforementioned element tin, yet, take differing numbers of neutrons in their nucleus. For example, stable helium atoms exist that contain either one or two neutrons, but both atoms have 2 protons. These different types of helium atoms accept unlike masses (iii or iv atomic mass units ), and they are called isotopes. For any given isotope, the sum of the numbers of protons and neutrons in the nucleus is called the mass number. This is considering each proton and each neutron weigh i atomic mass unit (amu). By adding together the number of protons and neutrons and multiplying by i amu, you can calculate the mass of the atom. All elements exist as a drove of isotopes. The discussion 'isotope' comes from the Greek 'isos' (meaning 'aforementioned') and 'topes' (meaning 'place') because the elements tin can occupy the same place on the periodic table while beingness different in subatomic construction.

Lithium Atom: Stylized lithium-seven atom: 3 protons (red), iv neutrons (black), and 3 electrons (blue). (Lithium also has another, rarer isotope with but 2 neutrons.)

Calculating Average Diminutive Mass

The boilerplate diminutive mass of an element is the sum of the masses of its isotopes, each multiplied past its natural affluence (the decimal associated with percent of atoms of that element that are of a given isotope).

Average atomic mass = f_oneOne thousand₁ + f₂M₂ +… + f_northwardM_n where f is the fraction representing the natural affluence of the isotope and M is the mass number (weight) of the isotope.

The average diminutive mass of an chemical element can be found on the periodic table, typically under the elemental symbol. When data are available regarding the natural abundance of various isotopes of an element, it is simple to calculate the average atomic mass.

• For helium, there is approximately ane isotope of Helium-three for every meg isotopes of Helium-four; therefore, the average atomic mass is very close to 4 amu (4.002602 amu).
• Chlorine consists of two major isotopes, ane with eighteen neutrons (75.77 percent of natural chlorine atoms) and one with xx neutrons (24.23 percent of natural chlorine atoms). The diminutive number of chlorine is 17 (it has 17 protons in its nucleus).

To summate the average mass, first catechumen the percentages into fractions (divide them by 100). And then, calculate the mass numbers. The chlorine isotope with 18 neutrons has an abundance of 0.7577 and a mass number of 35 amu. To calculate the average atomic mass, multiply the fraction by the mass number for each isotope, then add them together.

Average atomic mass of chlorine = (0.7577 [latex]\cdot[/latex] 35 amu) + (0.2423 [latex]\cdot[/latex] 37 amu) = 35.48 amu

Another instance is to calculate the diminutive mass of boron (B), which has two isotopes: B-10 with xix.9% natural abundance, and B-11 with fourscore.1% abundance. Therefore,

Average atomic mass of boron = (0.199 [latex]\cdot[/latex] 10 amu) + (0.801 [latex]\cdot[/latex]  11 amu) = 10.fourscore amu

Whenever we do mass calculations involving elements or compounds (combinations of elements), we always employ average diminutive masses.

Mass Spectrometry to Mensurate Mass

Mass spectrometry is a powerful characterization method that identifies elements, isotopes, and compounds based on mass-to-charge ratios.

Learning Objectives

Define the primary application of a mass spectrometer

Cardinal Takeaways

Central Points

• Mass spectrometers piece of work on samples in a gaseous state.
• The gaseous samples are ionized by an ion source, which adds or removes charged particles ( electrons or ions). Examples of ion sources include inductively coupled plasma and electron affect.
• Mass analyzers divide ionized samples according to their mass-to-charge ratio. Time-of-flight and quadrupole are examples of mass analyzers.
• A particle's mass can be calculated very accurately based on parameters such as how long information technology takes to travel a certain distance or its angle of travel.
• Mass spectrometers are so authentic that they can determine the types of elements in a compounds or measure the differences betwixt the mass of different isotopes of the aforementioned atom.

Key Terms

• ionization: Whatsoever process that leads to the dissociation of a neutral atom or molecule into charged particles (ions).
• plasma: A state of matter consisting of partially ionized gas, usually at high temperatures.
• mass-to-accuse ratio: The best way to split ions in a mass spectrometer. This number is calculated by dividing the ions weight past its accuse.

Mass spectrometry (MS) is a powerful technique that can identify a broad variety of chemical compounds. It is used to determine a particle'due south mass, the elemental limerick of a sample, and the chemical structures of larger molecules.

Mass spectrometers separate compounds based on a property known as the mass-to-charge ratio: the mass of the atom divided past its charge. Kickoff, the sample is ionized. Ionization is the procedure of converting an atom or molecule into an ion by adding or removing charged particles such equally electrons or ions. One time the sample is ionized, it is passed through some form of electric or magnetic field. A particle'south mass tin can be calculated based on parameters such equally how long information technology takes to travel a certain distance or its angle of travel.

Schematic of Mass Spectrometer: A sample is loaded onto the mass spectrometer, where it undergoes vaporization and ionization. The components of the sample are ionized past one of a diversity of methods, such as the ionizing filament. The ions are separated in an analyze past magnetic fields. They are separated according to their mass-to-charge ratios. The ions are detected, ordinarily by a quantitative method such as a Faraday collector. The ion signal is candy into a mass spectrum.

The Make-Up of Mass Spectrometry (MS) Instruments

MS instruments consist of two primary components:

• An ion source, which tin convert sample molecules into ions
• A mass analyzer, which sorts the ions past mass by applying electromagnetic fields

There are a broad variety of techniques for ionizing and detecting compounds.

Ionizing Compounds

Inductively coupled plasma (ICP) flame: Flick of an ICP flame viewed through green welder'south glass.

The ion source is the function of the mass spectrometer that ionizes the compound. Depending on the information desired from mass spectrometry analysis, unlike ionization techniques may be used. For instance, the most common ion source for analyzing elements is inductively coupled plasma (ICP). In ICP, a 10,000-degree C "flame" of plasma gas is used to atomize sample molecules and strip the outer electrons from those atoms.

The plasma is commonly generated from argon gas. Plasma gas is electrically neutral overall, simply a substantial number of its atoms are ionized past the loftier temperature.

Electron affect (EI) is another method for generating ions. In EI, the sample is heated until it becomes a gas. It is then passed through a beam of electrons. This high-energy axle strips electrons from the sample molecules, leaving backside a positively charged radical species.

Mass Analyzers

Mass analyzers separate the ions co-ordinate to their mass-to-charge ratios. At that place are many types of mass analyzers. Each has its strengths and weaknesses, including:

• how accurately they can measure similar mass-to-charge ratios
• the range of masses and sample concentrations they can measure out.

For example, a time-of-flight (TOF) analyzer uses an electric field to accelerate the ions through the same potential and and so measures the time they take to attain the detector. Since the particles all have the same accuse, their velocities depend but on their masses, and lighter ions will achieve the detector first.

Time-of-Flight mass analyzer: Schematic of a time-of-flight (TOF) mass analyzer.

Some other blazon of detector is a quadrupole. Here, ions are passed through four parallel rods, which utilise a varying electric voltage. Every bit the field changes, ions reply by following complex paths. Depending on the applied voltage, merely ions of a certain mass-to-charge ratio volition pass through the analyzer. All other ions will exist lost by collision with the rods.

Using a Mass Spectrometer to Measure out Mass

Here is how a mass spectrometer would analyze a sample of sodium chloride (table table salt).

• In the ion source, the sample is vaporized (turned into gas) and ionized into sodium (Na⁺) and chloride (Cl^–) ions.
• Sodium atoms and ions take only one isotope and a mass of most 23 amu.
• Chloride atoms and ions come in two isotopes, with masses of approximately 35 amu (at a natural abundance of about 75 percent) and approximately 37 amu (at a natural abundance of about 25 percent).
• The mass analyzer part of the spectrometer contains electric and magnetic fields, which exert forces on ions traveling through these fields. The angle at which the ion moves through the fields depends on its mass-to-charge ratio: lighter ions modify direction more than heavier ions.
• The streams of sorted ions pass from the analyzer to the detector, which records the relative affluence of each ion blazon. This information is used to make up one's mind the chemical composition of the original sample (i.eastward. that both sodium and chlorine are present in the sample) as well as its isotopic composition (the ratio of chlorine-35 to chlorine-37).

Source: https://courses.lumenlearning.com/boundless-chemistry/chapter/atomic-mass/#:~:text=For%20any%20given%20isotope%2C%20the,the%20mass%20of%20the%20atom.

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