Unit 11: The Atomic Nature of Matter

Collisions with moving atoms.

Brownian motion is caused by collisions between tiny dust specs or soot grains (visible through a microscope) and fast-moving invisible atoms (or molecules) in a gas or liquid. Brownian motion demonstrates the existence of atoms, as well as their perpetual erratic motion.

A nucleon is a proton or neutron.

The components of the nucleus are called nucleons, which consist of positively charged protons and uncharged neutrons. Note that a proton and a neutron have approximately equal masses.

A, B, D, C.

By referring to the periodic table, you can calculate the mass number of each molecule in Figure Q11.38: \begin{align} \text{A. } & \text{Oxygen molecule,}\; \text{O}_2 \text{:} & 2 \times 16 = 32 \nonumber\\ \text{B. } & \text{Water molecule,}\; \text{H}_2\text{O} \text{:} & (2 \times 1) + 16 = 18 \nonumber\\ \text{C. } & \text{Methane molecule,}\; \text{CH}_4 \text{:} & 12 + (4 \times 1) = 16 \nonumber\\ \text{D. } & \text{Ammonia molecule,}\; \text{NH}_3 \text{:} & 14 + (3 \times 1) = 17 \nonumber\\ \end{align}

One

The term element refers to a substance composed of a single type of atom. Therefore, an element (such as oxygen, mercury, or gold) cannot be broken down into simpler substances. It is possible, however, for the sample to include different isotopes of the same element.

Because of the many collisions of the perfume-vapor molecules with the air molecules.

Although a perfume-vapor molecule may have a relatively high speed, its path is full of obstacles. It continuously bumps into air molecules that are moving in random directions, causing the perfume-vapor molecule to change its speed and direction of motion after each collision. So, overall, perfume-vapor molecules that are initially more localized diffuse through air more slowly than the speed of individual molecules.

There are three elements and seven atoms.

A sulfuric acid molecule (H₂SO₄) consists of two atoms of the hydrogen element, one atom of the sulfur element, and four atoms of the oxygen element.

1. Cobalt-59 has 27 protons and 32 neutrons. Cobalt-60 has 27 protons and 33 neutrons.
2. 27.

1. Referring to the periodic table, you see that the atomic number for the element of cobalt is 27, which is equal to the number of protons inside the nucleus. Since all isotopes of cobalt have 27 protons in their nuclei, the lighter isotope (mass number 59) has $59 - 27 = 32\,\text{neutrons}$ and the heavier isotope (mass number 60) has $60 - 27 = 33\,\text{neutrons.}$
2. For an atom to be neutral, the number of electrons must be equal to the number of protons. Therefore, any neutral isotope of cobalt must have 27 electrons.

Ne, Ar, Kr, Xe, and Rn.

Elements with similar properties are located in the same column in the periodic table. The five other inert gases are located in the last column under helium: neon (Ne), argon (Ar), krypton (Kr), xenon (Xe), and radon (Rn).

In the periodic table of the elements, look up the mass number for each atom.

The kinetic energy of a particle of mass $m$ and speed $v$ is calculated using the formula \begin{equation} \text{KE} = \frac{1}{2} m v^2 \end{equation} Since the mass of a carbon atom is 12 times greater than the mass of a hydrogen atom, their kinetic energies also differ by the same ratio when the atoms are moving at the same speed. The carbon atom therefore has greater kinetic energy.

The 1 kg of aluminum contains more atoms. The mass number of aluminum is 27, while for lead it is 208. Since the lead atom is approximately eight times heavier than the aluminum atom, 1 kg of aluminum has about eight times more atoms that 1 kg of lead.

This claim is not accurate.

A certain amount of antimatter of mass $m$ will annihilate with only an equal amount of matter and convert to radiation. The total radiation energy released as a result is equal to $2 m c^2$.

Suppose the mass of the antimatter alien is 60 kg. The energy released as the alien steps on the ground would be \begin{equation} 2\, (60\,\text{kg})\, (3 \times 10^8\,\text{m/s})^2 = 1.1 \times 10^{19}\,\text{J} \nonumber \end{equation} This is an enormous amount of energy—more than 50 times the energy released when the Soviet Union detonated the 50-megaton Tsar Bomba on October 30, 1961. It would be a huge catastrophe, but the world would not explode into pure radiant energy.

A neutral atom carries an equal number of protons and electrons, which results in zero net charge on the atom. Since the electron carries a negative charge, an extra electron transforms a neutral atom into a negatively charged ion. A positive ion is produced when a neutral atom loses an electron.

Nitrogen-14

When two protons are added to the nucleus of an element, its atomic number increases by two. Since the atomic number of boron is 5, the resulting atom after adding two protons is that of nitrogen (atomic number 7).

Also, when two protons and one neutron (i.e., three nucleons) are added to a boron-11 nucleus, its mass number increases by three. Therefore, the mass number of the resulting nitrogen nucleus is $11 + 3 = 14$. \begin{align} \text{Boron-} &11 \nonumber\\[6pt] &\Downarrow\; \text{add two protons} \nonumber\\[6pt] \text{Nitrogen-} &13 \nonumber\\[6pt] & \Downarrow\; \text{add one neutron} \nonumber\\[6pt] \text{Nitrogen-} &14 \nonumber \end{align}