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Masses of isotopes

Due to the huge differences between the mass of the electron and the mass of nucleons (proton and neutron), atomic mass is determined primarily by the number of its protons and neutrons. Nearly all atomic mass in concentrated in its nucleus.

Mass of a proton is approximately equal to mass of a neutron and amounts to 1 u (1 u = 1.66 Indeks górny .^. 10Indeks górny -24^-24 g). That is why its atomic mass expressed in units will be approximately equal to the number of nucleons in its atomic nucleus. It may be assumed that total mass of protons and neutrons, i.e. mass number, is numerically equal to the atomic mass expressed in atomic mass units [u]. There is a slight difference due to the mass deficit resulting from the difference between the sum of masses of individual components of the atomic nucleus and the resting mass of the nucleus as a whole. Therefore, part of the mass of the atomic nucleus components is converted into energy that binds nucleons in the atomic nucleus.

Using all the information provided above and a formula (atomic weight [u] = mass number Indeks górny .^. 1 u), it can be easily calculated that atomic weight of protium (${}^{\text{1}}\text{H}$) amounts to 1 u, atomic weight of deuterium (${}^{\text{2}}\text{H}$) is 2 u, and the one of tritium (${}^{\text{3}}\text{H}$) is equal to 3 u.

The average atomic weight of elements

Task 1

Watch presentation “Standard atomic weight of elements”. Note how to calculate average atomic weight of an element.

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Grafika slajdu prezentacja, na slajdzie tekst: Standard atomic mass of elements.

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Grafika slajdu prezentacji. Na slajdzie tytuł: The formula to calculate the standard atomic mass of the element, poniżej wzór em indeks dolny at kropka równa się, w liczniku A jeden raz iks jeden procent plus a dwa razy iks dwa procent plus trzy kropki, w mianowniku 100 procent.

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Grafika slajdu prezentacji. Na slajdzie tytuł: Example 1, The isotopic composition of magnesium is: 78.70% indeks górny 24 em gie, 10.13% indeks górny 25 em gie, 11.17% indeks górny 26 em gie.

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Grafika slajdu, na slajdzie wzór. Em indeks dolny em gie równa się, w liczniku 23.985 u razy 78.70% plus 24.985 u razy 10.13% plus 25.983 u razy 11.17%, w mianowniku 100%. Wyliczona wartość Em indeks dolny em gie wynosi 24.309 u

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Grafika slajdu prezentacji. Na slajdzie tytuł: Ecample 2, the natural rubidium consist of two isotopes. wzór pierwszy: indeks górny 85 er be równa się 84.9177 u, wzór drugi: indeks górny 87 er be równa się 86,9085 u. Rubidium atomic mass is 85.4678 u.

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Grafika slajdu prezentacji. Na slajdzie wzory. Pierwszy wzór: indeks 85 er be iks %. Drugi wzór: indeks górny 87 er be w nawiasie 100 minus x, za nawiasem: procent

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Grafika slajdu prezentacji. Na slajdzie wzór: em indeks dolny at kropka równa się, w liczniku A jeden raz iks jeden procent plus a dwa razy iks dwa procent plus trzy kropki, w mianowniku 100 procent.

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Grafika slajdu prezentacji, na slajdzie wyliczenie. W liczniku 84.9117 u razy iks % plus 86.9085 u razy w nawiasie 100 minus iks, za nawiasem 5. W mianowniku 100 %. Dalej równa się 85.4678 u

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Grafika slajdu prezentacji, na slajdzie wyliczenie. W liczniku 84.9117 u razy iks % plus 86.9085 u razy w nawiasie 100 minus iks, za nawiasem 5. W mianowniku 100 %. Dalej równa się 85.4678 u razy 100

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Grafika slajdu. Na slajdzie wyliczenia. Pierwsze wyliczenie: 94.9117 u razy iks % plus 8690.85 u minus 86.9085 u razy iks % równa się 8546,78 u. Drugie wyliczenie: minus 1.9968 u razy iks % równa się minus 144.07 u podzielone przez minus 1.9968 u. Trzecie wyliczenie: iks % równa się 72.15. Czwarte wyliczenie: iks równa się 72.15 %

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The atomic weight stated in the periodic table is averaged. That is why fractional values are often assumed. It was taken into account that chemical elements consist of isotopes and each isotope has its share in atomic weight of given element.

Similarly, if you try to determine the average weight of students in the classroom based on information that 5% weigh 40 kg, 15% weigh 60 kg and others, i.e. 80% of students, weigh 50 kg. The average weight of all students would amount to 51 kg:

$\frac{5\%·40\mathrm{kg}+15\%·60\mathrm{kg}+80\%·50\mathrm{kg}}{100\%}=51\mathrm{kg}$

The result would be 51 kg although no student weighs 51 kg.
Similarly with chemical elements – the isotopic composition (percentage composition) of each of them is taken into account while calculating their average atomic masses. The following formula can be used to calculate average atomic mass of elements:

$\text{average atomic mass of an element = }\frac{{\text{mass of an isotope}}_{\text{1}}\text{ ·}{\text{ X}}_{\text{1}}\text{\% +}{\text{ mass of an isotope}}_{\text{2}}\text{ ·}{\text{ X}}_{\text{2}}\text{\% + . . . }{\text{+ mass of an isotope}}_{\text{n}}\text{ ·}{\text{ X}}_{\text{n}}\text{\% }}{\text{100\%}}$

where:
$\text{X\%}$ – percentage content of an isotope.

Using the above formula you can calculate average atomic mass of hydrogen:

$\text{average atomic mass of hydrogen = }\frac{\text{mass of an isotope }{}^{\text{1}}\text{H }\text{· percentage content of an isotope }{}^{\text{1}}\text{H}\text{ + mass of an isotope }{}^{\text{2}}\text{H }\text{· percentage content of an isotope }{}^{\text{2}}\text{H}}{\text{100\%}}$

$\frac{\text{1,00782503207(10) u · 99.985\% + 2,01410177785(36) u · 0.015\%}}{\text{100\%}}\text{= 1.008 u}$

Summary

• Isotopes are atoms of the same chemical element that have the same number of protons and different number of neutrons.

• Most natural chemical elements are a mixture of isotopes with a constant composition.

• Atomic weight of a chemical element is an average atomic mass obtained after taking into account its isotopic composition.

• Mass of an isotope is numerically approximately equal to its mass number due to the mass deficit resulting from the difference between the sum of masses of individual components of the atomic nucleus and the resting mass of the nucleus as a whole. Therefore, part of the mass of the atomic nucleus components is converted into energy that binds nucleons in the atomic nucleus.

Keywords

isotope, atom, proton, neutron, atomic weight

Glossary