2.1.4State the relative masses and relative charges of protons, neutrons and electrons. Calculate the number of protons, neutrons and electrons in atoms from the identity, mass number, atomic number and/or charge.

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2.1.5 State the position of protons, neutrons and electrons. Draw and interpret planetary models for elements up to Z=18.

The study of radioactive materials (elementsthat spontaneously give off particles to form new elements) by Frederick Soddy gave important clues about the internal structure of atoms. His work showed that some substanceswith different radioactive properties and different atomic weights were in fact the same element. He coined the termisotopefrom the Greek rootsisos (íσος “equal”) and topos (τóπος “place”). He described isotopes as, “identical outsides but different insides.” Soddy won the Nobel Prize in Chemistry in 1921 for his work.Therefore, not all atomsof a given element are identical.

Watch the following video for an introduction to isotopes: https://www.youtube.com/watch?v=GsJPxR6IfZI

DISCUSSION

## Isotopes and Mass numbers

Unlike the number of protons, which is always the same for all atoms of the same element, the number of neutrons can be different. Atoms of the same element with different numbers of neutrons are known asisotopes. Since the isotopes of any given element all contain the same number of protons, they have the same atomic number. However, since the isotopes of a given element contain different numbers of neutrons, different isotopes have different mass numbers.

Review the following two examples to help clarify this point.

Example:What is the atomic number (Z) and the mass number (A) of an isotope of lithium containing 3 neutrons? A lithium atom contains 3 protons in its nucleus.

Given-atomic number (Z)= # of protons = 3# of neutrons = 3Solve-mass number (A)= # of protons + # of neutrons= 3 + 3 = 6

Example:What is the atomic number (Z) and the mass number (A) of an isotope of lithium containing 4neutrons? A lithium atom contains 3protons in its nucleus.

Given-atomic numberZ= # of protons = 3# of neutrons = 4Solve-mass number (A)= # of protons + # of neutrons= 3 + 4 = 7

Notice that because the lithium atom always has 3protons, the atomic number for lithium is alwaysZ= 3. The mass number, however, isA= 6for the isotope with 3neutrons, andA= 7for the isotope with 4neutrons. In nature, only certain isotopes exist. For instance, lithium exists as an isotope with 3neutrons and as an isotope with 4neutrons, but it doesn’t exists as an isotope with 2neutrons or as an isotope with 5neutrons.

This whole discussion of isotopes brings us back to our understanding of atomic theory. Based upon isotopes, atoms of a given element cannot all be identical. Atoms of a given element can have different numbers of neutrons, and therefore, different mass numbers. It turns out that elements found in nature exist as uniform mixtures with a constant ratio of their naturally occurring isotopes. In other words, a piece of lithium always contains both types of naturally occurring lithium (the type with 3neutrons and the type with 4neutrons). Moreover, it always contains the two in the same relative amounts (or “relative abundances”). In a chunk of lithium, 93% will always be lithium with 4neutrons, while the remaining 7% will always be lithium with 3neutrons.

## Isotope Notation

Because the nucleus for an element can differ for the same element, we need to specify or be able to calculate the atomic number (Z) and the mass number (A) for that atom. The atom can be shown with anuclear symbol which takes the form

where X is the chemical symbol for the element, Ais themass number, and Zis the atomic number. For example, a nitrogen nucleus containing 7 protons and 8 neutrons would beSince all nitrogenatomsmust have 7 protons in their nucleus, sometimes the 7 is omitted and the symbol is written simply asThis same practice can be applied when writing the name. Omit the number of protons (or atomic number) and identify the mass number after the name and hyphen, for example, nitrogen-15.

For another example, let"s consider hydrogen"s three isotopes. All hydrogen atoms must have exactly 1 proton in the nucleus. However, the number of neutrons in the nucleus can vary, leading to different mass numbers (see the image below).

One isotope of hydrogen has 1 proton and 0 neutrons in the nuclues (in the image on the left above). The nuclear symbol is written above and has the name hydrogen-1. Another isotope of hydrogenhas 1 proton and 1 neutron in the nuclues (in the image in the center above). The nuclear symbol is written above and has the name hydrogen-2.A third isotope of hydrogenhas 1 proton and 2 neutrons in the nuclues (in the image on the right above). The nuclear symbol is written above and has the name hydrogen-3. (Unlike many other isotopes, isotopes of hydrogen are also referred to with specialized names. The hydrogen-1 may also be referred to as protium, hydrogen-2 as deuterium, and hydrogen-3 as tritium.)

Atomic Mass

Knowing about the different isotopes is important when it comes to calculating atomic mass. Theatomic mass(sometimes referred to as atomic weight) of an element is the weighted average mass of the atoms in a naturally occurring sample of the element.Atomic mass is typically reported in atomic mass units(amu).Most periodic tables give the atomic mass of each element. The atomic mass is often a decimal number usually written below the chemical symbol of each element in the table.

Isotope Abundance

It is possible to calculate the atomic mass of an element, provided you know the relative abundances the element’s naturally occurring isotopes and the masses of those different isotopes. The examples below show how this calculation is done.

Example:

Boron has two naturally occurring isotopes. In a sample of boron, 20% of the atoms are boron-10, which is an isotope of boron with 5 neutrons and a mass number of 10 amu. The other 80% of the atoms are boron-11, which is an isotope of boron with 6 neutrons and a mass number of 11 amu. What is the atomic mass of boron?

Solution:

To do this problem, we will calculate 20% of the mass of boron-10, which is how much the boron-10 isotope contributes to the “average boron atom.” We will also calculate 80% of the mass of boron-11, which is how much the boron-11 isotope contributes to the “average boron atom.”

Step One:Convert the percentages given in the question into their decimal forms by dividing each percentage by 100%:

Decimal form of 20% = 0.20Decimal form of 80% = 0.80

Step Two:Multiply the mass of each isotope by its relative abundance (percentage) in decimal form:

20% of the mass of boron-10 = 0.20 x 10 amu = 2.00 amu80% of the mass of boron-11 = 0.80 x 11 amu = 8.80 amu

Step Three:Find the total mass of the “average atom” by adding together the contributions from the different isotopes:

Total mass of average atom = 2.00 amu + 8.80 amu = 10.80 amu

The mass of an average boron atom, and thus boron’s atomic mass, is 10.80 amu.

Example:

Neon has three naturally occurring isotopes. In a sample of neon, 90.48% of the atoms are neon-20, which is an isotope of neon with 10 neutrons and a mass number of 19.99 amu. Another 0.27% of the atoms areneon-21, which is an isotope of neon with 11 neutrons and a mass number of 20.99 amu. The final 9.25% of the atoms areneon-22, which is an isotope of neon with 12 neutrons and a mass number of 21.99 amu. What is the atomic mass of neon?

Solution:

To do this problem, we will calculate 90.48% of the mass of neon-20, which is how muchneon-20 contributes to the “average neon atom.” We will also calculate 0.27% of the mass ofneon-21 and 9.25% of the mass ofneon-22, which are how much theneon-21 and theneon-22 isotopes contribute to the “average neon atom” respectively.

Step One:Convert the percentages given in the question into their decimal forms by dividing each percentage by 100%:

Decimal form of 90.48% = 0.9048Decimal form of 0.27% = 0.0027Decimal form of 9.25% = 0.0925

Step Two:Multiply the mass of each isotope by its relative abundance (percentage) in decimal form:

90.48% of the mass ofneon-20 =0.9048 x 20 amu = 18.10 amu0.27% of the mass of neon-21 = 0.0027 x 21 amu = 0.057 amu9.25% of the mass ofneon-22 = 0.0925 x 22 amu = 2.04 amu

Step Three:Find the total mass of the “average atom” by adding together the contributions from the different isotopes:

Total mass of average atom = 18.10 amu + 0.057 amu + 2.04 amu

The mass of an average neon atom, and thus neon’s atomic mass, is 20.20 amu.

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Notice that atomic mass from the periodic table for boron (symbol B) is 10.81 and the atomic mass of neon (symbol Ne) is 20.18, both which are very close to what we calculated in our examples. Take time to notice that not all periodic tables have the atomic number above the element’s symbol and the atomic mass below it. If you are ever confused, remember that the atomic number is always a whole number and should always be the smaller of the two, while the atomic mass for most numbers is in decimal form and should always be the larger of the two. (The atomic mass must include both the number of protons and the average number of neutrons.)

Bohr Model

As mentioned previously,the Bohr model is useful for visualizing the placement of the protons, neutrons, and electrons in the atom of an element. With the variation of neutrons in isotopes, the Bohr model of the atom must change - but only slightly. For example, consider an atom of sulfur with a mass number of 32, sulfur-32 (see image below),

and an atom of sulfur with a mass number of 33, sulfur-33. The similarities between the isotopes would be the atom identity, therefore, the atomic number (16) and # of protons (16) remain the same. Since it is an atom of sulfur, the proton # (16) still equals the electron # (16). The two major differences in the Bohr model diagrams would be the mass number and # of neutrons. The calculation of mass number = # of protons + # of neturons, therefore,mass number (33) = # of protons (16) + # of neturons (?). Neturon #, then = 17 (see image below).