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Chapter 42: Problem 73

The nuclide \({ }^{14} \mathrm{C}\) contains (a) how many protons and (b) how many neutrons?

Short Answer

Expert verified
(a) 6 protons, (b) 8 neutrons.

Step by step solution

01

Identify the Element

The element symbol for \({ }^{14} \text{C}\) is \text{C}\, which stands for carbon. Carbon is located on the periodic table with an atomic number of 6.
02

Determine the Number of Protons

The atomic number of carbon is 6, which means it has 6 protons. The atomic number of an element always tells you how many protons are in the nucleus of the atom.
03

Calculate the Number of Neutrons

The mass number of the nuclide \({ }^{14} \text{C}\) is 14. To find the number of neutrons, subtract the number of protons (6) from the mass number (14). This gives: \ 14 - 6 = 8 \; therefore, there are 8 neutrons.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Protons
In the world of atomic structure, protons play a pivotal role. They are positively charged particles that reside in the nucleus of an atom. The number of protons within an atom's nucleus determines the element itself. For instance, carbon atoms will always have 6 protons. This is because the atomic number, which is the identity tag of elements on the periodic table, reflects the number of protons. Each element has a unique atomic number.
  • The proton count doesn't change for a given element.
  • Protons contribute significantly to an atom's overall mass.
  • The presence of protons results in positive charges.
Therefore, when you see the symbol \(^{{14}} \ ext{C}\), despite the 14 in the upper left corner which indicates the mass number, the 6 protons of carbon are constant and critical for defining the element.
Neutrons
Neutrons, unlike protons, have no electrical charge. They also reside in the nucleus alongside protons. Their primary role involves adding mass and stability to the atom. While protons define the element, neutrons can vary within atoms of the same element without changing what element it is. These variants are known as isotopes.
  • Neutrons help hold the nucleus together through nuclear forces.
  • Isotopes possess different numbers of neutrons.
  • Neutrons contribute to the overall atomic mass.
For carbon's isotope \(^{{14}} \ ext{C}\), by subtracting the number of protons from the mass number (14 - 6), we find there are 8 neutrons. These isotopes, while varied in neutron number, will always belong to the same element on the table as long as they share the same proton count.
Mass Number
The mass number of an atom provides significant insight into its composition. It is the sum of protons and neutrons within the atomic nucleus. While the atomic number reveals the number of protons and the identity of the element, the mass number offers a glimpse into the isotope present. For example, in the nuclide \(^{{14}} \ ext{C}\), the mass number is 14.
  • The mass number is not found directly on the periodic table.
  • It is represented typically at the top left when indicating specific isotopes.
  • A change in mass number often means a different isotope with the same proton count but a different neutron count.
It鈥檚 crucial to remember that the mass number is a whole number. Unlike atomic mass (which is often a decimal), it reflects the integer nature of how many protons and neutrons combine within the nucleus to form that specific isotope.

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Most popular questions from this chapter

What is the activity of a \(10 \mathrm{ng}\) sample of \({ }^{92} \mathrm{Kr}\), which has a halflife of \(1.84 \mathrm{~s}\) ?

What is the binding energy per nucleon of the americium isotope \({ }_{95}^{244} \mathrm{Am} ?\) Here are some atomic masses and the neutron mass. \(\begin{array}{lrrr}{ }_{95}^{244} \mathrm{Am} & 244.064279 \mathrm{u} & { }^{1} \mathrm{H} & 1.007825 \mathrm{u} \\ \mathrm{n} & 1.008665 \mathrm{u} & & \end{array}\)

A radioactive isotope of mercury, \({ }^{197} \mathrm{Hg}\), decays to gold, \({ }^{197} \mathrm{Au}\), with a disintegration constant of \(0.0108 \mathrm{~h}^{-1}\). (a) Calculate the half-life of the \({ }^{197} \mathrm{Hg}\). What fraction of a sample will remain at the end of (b) three half-lives and (c) \(10.0\) days?

A radioactive sample intended for irradiation of a hospital patient is prepared at a nearby laboratory. The sample has a halflife of \(83.61 \mathrm{~h}\). What should its initial activity be if its activity is to be \(7.4 \times 10^{8} \mathrm{~Bq}\) when it is used to irradiate the patient \(24 \mathrm{~h}\) later?

A radioactive nuclide has a half-life of \(30.0 \mathrm{y}\). What fraction of an initially pure sample of this nuclide will remain undecayed at the end of (a) \(60.0 \mathrm{y}\) and (b) \(90.0 \mathrm{y}\) ?
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