Question

Indicate the number of protons and neutrons in the following nuclei: \((\mathbf{a}) _{53}^{129} I,(\mathbf{b})^{138} \mathrm{Ba},(\mathbf{c})\) neptunium\(-237 .\)

Short answer

For each nucleus: \[\textrm{(a)}\ (\textrm{I})\ \textrm{53 protons, 76 neutrons}\] \[\textrm{(b)}\ (\textrm{Ba})\ \textrm{56 protons, 82 neutrons}\] \[\textrm{(c)}\ (\textrm{Np-237})\ \textrm{93 protons, 144 neutrons}\]

Step-by-step solution

Nucleus (a) - \(_{53}^{129} I\)

For the given nucleus \(_{53}^{129} I\), the subscript '53' denotes the number of protons present in the nucleus. The superscript '129' denotes the atomic mass number (A), which is the sum of protons and neutrons in the nucleus. To find the number of neutrons in this nucleus, we can use the formula: Neutrons = A - number of protons In this case: Neutrons = \(129 - 53\) Neutrons = 76 Result for nucleus (a): There are 53 protons and 76 neutrons.

Nucleus (b) - \(^{138} \mathrm{Ba}\)

For the given nucleus \(^{138} \mathrm{Ba}\), we need to identify the number of protons for barium (Ba) from the periodic table. Barium has the atomic number (Z) of 56, which means that there are 56 protons in its nucleus. The superscript '138' denotes the atomic mass number (A), which is the sum of protons and neutrons in the nucleus. To find the number of neutrons in this nucleus, we can use the formula: Neutrons = A - number of protons In this case: Neutrons = \(138 - 56\) Neutrons = 82 Result for nucleus (b): There are 56 protons and 82 neutrons.

Nucleus (c) - Neptunium-237

For the given nucleus Neptunium-237, we need to identify the number of protons for neptunium from the periodic table. Neptunium has the atomic number (Z) of 93, which means that there are 93 protons in its nucleus. The number '237' after the hyphen denotes the atomic mass number (A), which is the sum of protons and neutrons in the nucleus. To find the number of neutrons in this nucleus, we can use the formula: Neutrons = A - number of protons In this case: Neutrons = \(237 - 93\) Neutrons = 144 Result for nucleus (c): There are 93 protons and 144 neutrons.

Key concepts

Atomic Structure

Atoms are the building blocks of matter, and their structure is fundamental in understanding nuclear chemistry. An atom consists of a dense central nucleus surrounded by a cloud of electrons. At the core of every atom is its nucleus, which contains protons and neutrons. These subatomic particles define the characteristics of the atom. The nucleus is incredibly small compared to the overall size of the atom, but it contains most of the atom's mass.

The atomic structure can be described by two key numbers:

• Atomic Number (Z): This is the number of protons in an atom's nucleus, and it defines the element. For example, an element with 53 protons will always be iodine.
• Mass Number (A): This is the total number of protons and neutrons in the nucleus. It gives an indication of the atom's mass and plays a key role in identifying the isotope of an element.

To find the number of neutrons in an atom, you subtract the atomic number from the mass number, which is reflected in the formula: \[\text{Neutrons} = A - Z\] Understanding atomic structure helps in identifying and differentiating isotopes, which are atoms of the same element with different numbers of neutrons.

Protons

Protons are positively charged particles found in the nucleus of an atom. Each proton carries a charge of +1, and they play a crucial role in defining the identity of an element. The number of protons, or the atomic number, is unique to each element and determines the element's position on the periodic table.

For example, if an atom contains 53 protons, it is definitely iodine (I) because iodine's atomic number is 53. Similarly, if an atom has 56 protons, it is barium (Ba), and if it has 93 protons, it is neptunium (Np). Hence, the number of protons is vital in maintaining the identity of the atom.

Protons contribute to the atom's overall mass and are tightly bound in the nucleus alongside neutrons through the strong nuclear force. This force is among the strongest known and prevents the positively charged protons from repelling each other within the nucleus. Understanding protons not only helps in identifying elements but also in studying other properties like isotopic variations.

Neutrons

Neutrons are electrically neutral particles residing in the nucleus along with protons. They have no charge, which means they don't affect the atom's charge but significantly contribute to its mass. The number of neutrons, paired with the number of protons, defines the isotope of an element.

The difference in the number of neutrons among isotopes gives rise to variations in their physical properties, such as stability and radioactive behavior. For instance, the variations among isotopes of iodine, barium, and neptunium illustrate how the differences in neutron counts contribute to diverse nuclear properties and applications.

Neutrons are pivotal in nuclear chemistry because they can influence nuclear reactions. They act as stabilizing forces, and a different neutron count can make a nucleus more stable or unstable, potentially leading to radioactive decay.

The calculation to determine the number of neutrons in an atom is straightforward: subtract the atomic number from the mass number:\[\text{Neutrons} = A - Z\] This simple process is essential for the study of nuclear reactions, including fission and fusion, and for tailoring nuclear materials for various scientific and industrial purposes.