How To Find The Mass Number Of An Isotope

Average Atomic Mass

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

Learning Objectives

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

Key Takeaways

Key Points

An chemical element can take differing numbers of neutrons in its nucleus, but it always has the same number of protons. The versions of an chemical element with different neutrons have dissimilar masses and are chosen isotopes.
The average diminutive mass for an element is calculated by summing the masses of the element'south isotopes, each multiplied by its natural abundance on Earth.
When doing any mass calculations involving elements or compounds, ever utilise average atomic mass, which can be found on the periodic table.

Key Terms

mass number: The full 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's isotopes, each multiplied past its natural affluence on Earth.

The diminutive number of an element defines the chemical element'south identity and signifies the number of protons in the nucleus of one cantlet. For instance, the element hydrogen (the lightest chemical element) will ever accept 1 proton in its nucleus. The chemical element helium volition always have 2 protons in its nucleus.

Isotopes

Atoms of the same element can, withal, have differing numbers of neutrons in their nucleus. For example, stable helium atoms be that incorporate either one or two neutrons, but both atoms take 2 protons. These dissimilar types of helium atoms have dissimilar masses (3 or 4 diminutive mass units ), and they are chosen isotopes. For whatever given isotope, the sum of the numbers of protons and neutrons in the nucleus is called the mass number. This is because each proton and each neutron counterbalance one atomic mass unit (amu). By calculation together the number of protons and neutrons and multiplying by 1 amu, you can summate the mass of the cantlet. All elements exist every bit a collection of isotopes. The word 'isotope' comes from the Greek 'isos' (pregnant 'aforementioned') and 'topes' (significant 'place') because the elements tin occupy the aforementioned place on the periodic table while beingness different in subatomic construction.

Lithium Atom: Stylized lithium-7 cantlet: 3 protons (cherry-red), 4 neutrons (black), and 3 electrons (blue). (Lithium likewise has another, rarer isotope with just two neutrons.)

Calculating Average Atomic Mass

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

Average atomic mass = f₁M_i + f_twoM₂ +… + f_{due north}Chiliad_nwhere f is the fraction representing the natural abundance of the isotope and Grand is the mass number (weight) of the isotope.

The boilerplate atomic mass of an chemical element tin can exist found on the periodic table, typically under the elemental symbol. When data are available regarding the natural affluence of various isotopes of an element, it is elementary to calculate the boilerplate atomic mass.

For helium, at that place is approximately one isotope of Helium-3 for every meg isotopes of Helium-4; therefore, the boilerplate diminutive mass is very shut to 4 amu (4.002602 amu).
Chlorine consists of two major isotopes, one with xviii neutrons (75.77 percent of natural chlorine atoms) and one with 20 neutrons (24.23 percent of natural chlorine atoms). The atomic number of chlorine is 17 (it has 17 protons in its nucleus).

To calculate the average mass, first catechumen the percentages into fractions (divide them by 100). So, summate 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 past the mass number for each isotope, then add them together.

Average diminutive 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 atomic mass of boron (B), which has two isotopes: B-x with xix.9% natural abundance, and B-xi with lxxx.1% affluence. Therefore,

Average atomic mass of boron = (0.199 [latex]\cdot[/latex] 10 amu) + (0.801 [latex]\cdot[/latex] eleven amu) = 10.80 amu

Whenever we do mass calculations involving elements or compounds (combinations of elements), we always use average atomic 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

Ascertain the main awarding of a mass spectrometer

Cardinal Takeaways

Key Points

Mass spectrometers piece of work on samples in a gaseous state.
The gaseous samples are ionized past an ion source, which adds or removes charged particles ( electrons or ions). Examples of ion sources include inductively coupled plasma and electron impact.
Mass analyzers separate ionized samples according to their mass-to-charge ratio. Time-of-flight and quadrupole are examples of mass analyzers.
A particle'southward mass can be calculated very accurately based on parameters such as how long it takes to travel a sure distance or its angle of travel.
Mass spectrometers are so accurate that they can determine the types of elements in a compounds or measure out the differences between the mass of different isotopes of the same cantlet.

Central Terms

ionization: Any process that leads to the dissociation of a neutral cantlet or molecule into charged particles (ions).
plasma: A land of matter consisting of partially ionized gas, usually at high temperatures.
mass-to-charge ratio: The best style to separate ions in a mass spectrometer. This number is calculated past dividing the ions weight by its charge.

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

Mass spectrometers dissever compounds based on a belongings known every bit the mass-to-charge ratio: the mass of the atom divided past its charge. First, the sample is ionized. Ionization is the process of converting an atom or molecule into an ion by adding or removing charged particles such as electrons or ions. In one case the sample is ionized, it is passed through some form of electric or magnetic field. A particle's mass tin can be calculated based on parameters such as how long it takes to travel a certain distance or its angle of travel.

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

The Make-Up of Mass Spectrometry (MS) Instruments

MS instruments consist of two master components:

An ion source, which can catechumen sample molecules into ions
A mass analyzer, which sorts the ions by mass by applying electromagnetic fields

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

Ionizing Compounds

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

The ion source is the part of the mass spectrometer that ionizes the chemical compound. Depending on the information desired from mass spectrometry assay, different ionization techniques may be used. For example, the nearly mutual ion source for analyzing elements is inductively coupled plasma (ICP). In ICP, a 10,000-caste C "flame" of plasma gas is used to disintegrate sample molecules and strip the outer electrons from those atoms.

The plasma is normally generated from argon gas. Plasma gas is electrically neutral overall, but a substantial number of its atoms are ionized by the high temperature.

Electron impact (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 loftier-energy beam strips electrons from the sample molecules, leaving behind a positively charged radical species.

Mass Analyzers

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

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

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

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

Another blazon of detector is a quadrupole. Hither, ions are passed through four parallel rods, which utilize a varying electrical voltage. Every bit the field changes, ions answer by post-obit complex paths. Depending on the applied voltage, just ions of a certain mass-to-charge ratio volition laissez passer through the analyzer. All other ions volition be lost by collision with the rods.

Using a Mass Spectrometer to Measure Mass

Here is how a mass spectrometer would clarify 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 have only one isotope and a mass of near 23 amu.
Chloride atoms and ions come in 2 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 pct).
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 than heavier ions.
The streams of sorted ions pass from the analyzer to the detector, which records the relative abundance of each ion type. This data is used to determine the chemic composition of the original sample (i.e. that both sodium and chlorine are present in the sample) also equally its isotopic composition (the ratio of chlorine-35 to chlorine-37).