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Chapter 30: Problem 1

I How many protons and how many neutrons are in (a) \({ }^{3} \mathrm{H}\) (b) \({ }^{40} \mathrm{Ar},(\mathrm{c})^{40} \mathrm{Ca},\) and (d) \(^{239} \mathrm{Pu} ?\)

Short Answer

Expert verified
_ For \({ }^{3} \mathrm{H}\), there are 1 proton and 2 neutrons. _ For \({ }^{40} \mathrm{Ar}\), there are 18 protons and 22 neutrons. _ For \({ }^{40} \mathrm{Ca}\), there are 20 protons and 20 neutrons. _ For \({ }^{239} \mathrm{Pu}\), there are 94 protons and 145 neutrons.

Step by step solution

01

Identify the Atomic and Mass Numbers

For each isotope, identify the atom's atomic number (which equals the number of protons) and mass number (which equals the number of protons and neutrons combined). _ For \({ }^{3} \mathrm{H}\), hydrogen (H) has an atomic number of 1 and a mass number of 3. _ For \({ }^{40} \mathrm{Ar}\), argon (Ar) has an atomic number of 18 and a mass number of 40. _ For \({ }^{40} \mathrm{Ca}\), calcium (Ca) has an atomic number of 20 and a mass number of 40. _ For \({ }^{239} \mathrm{Pu}\), plutonium (Pu) has an atomic number of 94 and a mass number of 239.
02

Calculate the Number of Protons

The atomic number is the same as the number of protons. So, the number of protons for each atom are: _ For \({ }^{3} \mathrm{H}\), protons = 1 _ For \({ }^{40} \mathrm{Ar}\), protons = 18 _ For \({ }^{40} \mathrm{Ca}\), protons = 20 _ For \({ }^{239} \mathrm{Pu}\), protons = 94
03

Calculate the Number of Neutrons

The number of neutrons is found by subtracting the number of protons from the mass number. So, the nuumber of neutrons for each atom are: _ For \({ }^{3} \mathrm{H}\), neutrons = 3 - 1 = 2 _ For \({ }^{40} \mathrm{Ar}\), neutrons = 40 - 18 = 22 _ For \({ }^{40} \mathrm{Ca}\), neutrons = 40 - 20 = 20 _ For \({ }^{239} \mathrm{Pu}\), neutrons = 239 - 94 = 145. The number of neutrons is often different even among atoms of the same element, these different atoms are called isotopes.

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Key Concepts

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

Understanding Isotopes
Isotopes are variants of a particular chemical element which differ in neutron number, though they have the same number of protons. The number of protons in an atom defines the element itself, while the number of neutrons can vary. This variance results in isotopes of an element.

For instance, hydrogen has isotopes like
  • Protium (\(^1_1\text{H}\)) 鈥� with 1 proton and no neutrons,
  • Deuterium (\(^2_1\text{H}\)) 鈥� with 1 proton and 1 neutron, and
  • Tritium (\(^3_1\text{H}\)) 鈥� with 1 proton and 2 neutrons.
Despite having different numbers of neutrons, these isotopes share chemical properties because chemical behavior is mostly determined by electron configuration and protons.
Defining Atomic Number
The atomic number of an element denotes the number of protons found in the nucleus of its atoms. It's a fundamental characteristic that defines the element.

For example:
  • Hydrogen has an atomic number of 1,
  • Argon has an atomic number of 18,
  • Calcium has an atomic number of 20, and
  • Plutonium has an atomic number of 94.
This identifier not only showcases the number of protons but also determines the position of the element in the periodic table and its general properties. Remember, changing the atomic number means you are changing the element itself.
Determining Mass Number
Mass number provides the total count of protons and neutrons in an atom's nucleus. It is not fixed for an element but varies with isotopes.

Consider the examples given:
  • \(^3\text{H}\) has a mass number of 3,
  • \(^40\text{Ar}\) has a mass number of 40,
  • \(^40\text{Ca}\) also has a mass number of 40,
  • \(^239\text{Pu}\) has a mass number of 239.
This is calculated as the sum of protons and neutrons, setting the stage for understanding isotopic variations. Different mass numbers illustrate the different nature of isotopes within an element.
Exploring Neutrons and Protons
Protons and neutrons make up the nucleus of an atom. Protons are positively charged, while neutrons carry no charge. These particles together determine the mass of an atom.

To compute the neutrons, you subtract the number of protons (the atomic number) from the mass number. Consider the calculations:
  • For \(^3\text{H}\), 3 (mass number) - 1 (proton) = 2 neutrons.
  • For \(^40\text{Ar}\), 40 (mass number) - 18 (protons) = 22 neutrons.
  • For \(^40\text{Ca}\), 40 (mass number) - 20 (protons) = 20 neutrons.
  • For \(^239\text{Pu}\), 239 (mass number) - 94 (protons) = 145 neutrons.
Recognizing the number of neutrons is vital, as it points to different isotopes and offers insight into nuclear stability and other nuclear properties.

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Most popular questions from this chapter

The Chernobyl reactor accident in what is now Ukraine was the worst nuclear disaster of all time. Fission products from the reactor core spread over a wide area. The primary radiation exposure to people in western Europe was due to the short-lived (half-life 8.0 days isotope \({ }^{131} \mathrm{I},\) which fell across the landscape and was ingested by grazing cows that concentrated the isotope in their milk. Farmers couldn't sell the contaminated milk, so many opted to use the milk to make cheese, aging it until the radioactivity decayed to acceptable levels. How much time must elapse for the activity of a block of cheese containing \({ }^{131} \mathrm{I}\) to drop to \(1.0 \%\) of its initial value?

The uranium isotope \({ }^{235} \mathrm{U}\) can fission - break into two smaller-mass components and free neutrons-if it is struck by a free neutron. A typical reaction is $$ { }_{0}^{1} \mathrm{n}+{ }_{92}^{235} \mathrm{U} \rightarrow{ }_{56}^{141} \mathrm{Ba}+{ }_{36}^{92} \mathrm{Kr}+3{ }_{0}^{1} \mathrm{n} $$ As you can see, the subscripts (the number of protons) and the superscripts (the number of nucleons) "balance" before and after the fission event; there is no change in the number of protons or Significant energy is released in this reaction. If a fission event happens in a large chunk of \({ }^{235} \mathrm{U},\) the neutrons released may induce the fission of other \({ }^{235} \mathrm{U}\) atoms, resulting in a chain reaction. This is how a nuclear reactor works. The number of neutrons required to create a stable nucleus increases with atomic number. When the heavy \({ }^{235} \mathrm{U}\) nucleus fissions, the lighter reaction products are thus neutron rich and are likely unstable. Many of the short-lived radioactive nuclei used in medicine are produced in fission reactions in nuclear reactors. What statement can be made about the masses of atoms in the above reaction? A. \(m\left({ }_{92}^{235} \mathrm{U}\right)>m\left({ }_{56}^{141} \mathrm{Ba}\right)+m\left({ }_{36}^{92} \mathrm{Kr}\right)+2 m\left({ }_{0}^{1} \mathrm{n}\right)\) B. \(m\left({ }_{92}^{235} \mathrm{U}\right)

The Curiosity rover sent to explore the surface of Mars has an electric generator powered by heat from the radioactive decay of \({ }^{238} \mathrm{Pu},\) a plutonium isotope that decays by alpha emission with a half- life of 88 years. At the start of the mission, the generator contained \(9.6 \times 10^{24}\) nuclei of \({ }^{238} \mathrm{Pu}\) What is the daughter nucleus of the decay? A. \({ }^{238} \mathrm{Am}\) \(\mathrm{B} .^{238} \mathrm{Pu}\) \(\mathrm{C} \cdot{ }^{238} \mathrm{Np}\) D. \({ }^{236} \mathrm{Th}\) \(\mathrm{E} .^{234} \mathrm{U}\)

Cobalt has one stable isotope, \(^{59}\) Co. What are the likely decay modes and daughter nuclei for (a) \({ }^{56}\) Co and (b) \(^{62} \mathrm{Co} ?\)

Positive and negative pions, denoted \(\pi^{+}\) and \(\pi^{-},\) are antiparticles of each other. Each has a rest mass of \(140 \mathrm{MeV} / \mathrm{c}^{2}\). Suppose a collision between an electron and positron, each with kinetic energy \(K\), produces a \(\pi^{+}, \pi^{-}\) pair. What is the smallest possible value for \(K ?\)
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