Understand The Nuclear Atom - IB Chemistry

Which statement best defines the relative atomic mass, $A_r$ , of an element?
Answer: The weighted average mass of an atom of the element compared to 1/12th the mass of an atom of carbon-12. The relative atomic mass ( $A_r$ ) is the weighted average mass of the naturally occurring isotopes of an element relative to a standard. The standard is 1/12th of the mass of a single neutral atom of carbon-12 in its ground state. Option A describes the mass number of an isotope. Option C describes the mass of a single atom in grams, not the relative mass. Option D is an imprecise description that omits the reference standard.
Gallium has a relative atomic mass of 69.72 and consists of two stable isotopes, $^{69}\text{Ga}$ and $^{71}\text{Ga}$ . A second element, Z, also has only two stable isotopes, $^{68}\text{Z}$ and $^{70}\text{Z}$ . If the percentage abundance of $^{68}\text{Z}$ is the same as the percentage abundance of $^{69}\text{Ga}$ , what is the relative atomic mass of element Z?
Answer: 68.72 First, find the abundance of $^{69}\text{Ga}$ . Let its fractional abundance be x. Then $69.72 = 69x + 71(1-x)$ . This gives $69.72 = 71 - 2x$ , so $2x = 1.28$ and $x = 0.64$ . The abundance of $^{69}\text{Ga}$ is 64%. The problem states the abundance of $^{68}\text{Z}$ is the same, so its abundance is 64%. The abundance of $^{70}\text{Z}$ must be 100% - 64% = 36%. The relative atomic mass of Z is the weighted average: $A_r(Z) = (68 \times 0.64) + (70 \times 0.36) = 43.52 + 25.20 = 68.72$ .
What is the total number of neutrons in a 3.40 g sample of ammonia gas ( $\text{NH}_3$ )? (Assume nitrogen is $^{14}\text{N}$ and hydrogen is $^{1}\text{H}$ . $N_A = 6.02 \times 10^{23} \text{ mol}^{-1}$ )
Answer: $8.43 \times 10^{23}$ 1. Molar mass of $\text{NH}_3 = 14.0 + 3(1.0) = 17.0 \text{ g mol}^{-1}$ . 2. Moles of $\text{NH}_3 = \frac{\text{mass}}{\text{molar mass}} = \frac{3.40 \text{ g}}{17.0 \text{ g mol}^{-1}} = 0.200 \text{ mol}$ . 3. Neutrons per molecule: $^{14}\text{N}$ has 14-7=7 neutrons. $^{1}\text{H}$ has 1-1=0 neutrons. Total per molecule = 7 + 3(0) = 7 neutrons. 4. Total neutrons = moles $\times$ Avogadro constant $\times$ neutrons per molecule = $0.200 \text{ mol} \times 6.02 \times 10^{23} \text{ mol}^{-1} \times 7 = 8.428 \times 10^{23}$ .
A particle has a mass number of 32, contains 16 neutrons, and possesses 18 electrons. Which of the following correctly identifies this particle?
Answer: A sulfide ion, $^{32}\text{S}^{2-}$ The number of protons (atomic number, Z) is calculated by subtracting the number of neutrons from the mass number: Z = 32 - 16 = 16. The element with Z=16 is Sulfur (S). The particle has 16 protons and 18 electrons. The charge is the number of protons minus the number of electrons: Charge = 16 - 18 = -2. Therefore, the particle is the sulfide ion, $^{32}\text{S}^{2-}$ .
Two atoms, P and R, undergo nuclear processes. Atom P has 26 protons and 30 neutrons initially. After beta-minus decay, the resulting nucleus captures 2 electrons to form an ion. Atom R starts with the same mass number as the final form of P but has 2 fewer neutrons. How many protons does atom R contain?
Answer: 29 protons in atom R's nuclear structure Atom P starts with 26 protons and 30 neutrons (mass number = 56). After beta-minus decay, a neutron converts to a proton, so the new nucleus has 27 protons and 29 neutrons (mass number still = 56). Atom R has the same mass number (56) but 2 fewer neutrons than P's final form, so R has 29 - 2 = 27 neutrons. Since mass number = protons + neutrons: 56 = protons + 27, so R has 56 - 27 = 29 protons.
An atom has 16 neutrons, and its most stable ion has a charge of 3- and contains 18 electrons. What is the mass number of this atom?
Answer: 31 The ion has a 3- charge, meaning it has gained 3 electrons to reach 18. The neutral atom therefore has 18 - 3 = 15 electrons. In a neutral atom, the number of electrons equals the number of protons, so the atomic number (Z) is 15. The mass number (A) is the sum of protons and neutrons: A = 15 (protons) + 16 (neutrons) = 31.
Which statement best explains why isotopes of an element can be separated using a mass spectrometer?
Answer: Isotopes form ions with different masses, which are deflected by different amounts in a magnetic field. In a mass spectrometer, atoms are ionized (usually to a +1 charge), accelerated by an electric field, and then deflected by a magnetic field. The amount of deflection depends on the mass-to-charge ratio (m/z). Since isotopes are ionized to the same charge, their separation is based on their different masses. Lighter ions are deflected more than heavier ions.
Which statement correctly explains why the mass number of a specific isotope is always an integer, while the relative atomic mass of an element is often not an integer?
Answer: Mass number is a count of nucleons in a single nucleus, whereas relative atomic mass is a weighted average of isotopic masses. The mass number (A) represents the total number of protons and neutrons (nucleons) in the nucleus of a single atom of a specific isotope. Since this is a count of particles, it is always an integer. The relative atomic mass ( $A_r$ ) of an element is the weighted average of the masses of its naturally occurring isotopes. Because it is an average of different isotopic masses with non-integer abundances, it is typically not an integer.
Consider the nuclear equation: $^{238}$ U → $^{234}$ Th + X. After this decay process occurs, a thorium atom gains 2 electrons to achieve a stable electron configuration. What is the neutron-to-proton ratio in the resulting thorium ion?
Answer: 1.61 neutrons per proton in the ionic species The decay shows $^{238}$ U (92 protons) → $^{234}$ Th + X, where X is an alpha particle. $^{234}$ Th has mass number 234 and atomic number 90 (thorium), so it has 90 protons and 234 - 90 = 144 neutrons. When the thorium atom gains 2 electrons, it becomes Th²⁻, but the nuclear composition doesn't change. The neutron-to-proton ratio remains 144/90 = 1.60 ≈ 1.61.
An ion X³⁺ has 10 electrons and its nucleus contains 14 neutrons. What is the correct nuclear symbol for this atom?
Answer: $^{27}_{13}\text{Al}$ The ion has a 3+ charge and 10 electrons. A neutral atom of X would therefore have 10 + 3 = 13 electrons, and thus 13 protons. The atomic number (Z) is 13, which corresponds to Aluminum (Al). The mass number (A) is the sum of protons and neutrons, which is 13 + 14 = 27. Therefore, the nuclear symbol is $^{27}_{13}\text{Al}$ .
An ion, X³⁺, has a mass number of 52 and contains 21 electrons. What is the composition of the nucleus of a neutral atom of X?
Answer: 24 protons and 28 neutrons The ion X³⁺ has a charge of +3, meaning it has 3 fewer electrons than protons. Since it has 21 electrons, the number of protons is 21 + 3 = 24. The atomic number (Z) is 24, which identifies the element as Chromium (Cr). The composition of the nucleus is determined by the number of protons and neutrons, which is the same for the ion and the neutral atom. The number of neutrons is the mass number minus the number of protons: 52 - 24 = 28. Therefore, the nucleus contains 24 protons and 28 neutrons.
A sample of boron is composed of two isotopes, $^{10}\text{B}$ and $^{11}\text{B}$ . If the relative atomic mass of the sample is 10.80, what is the percentage abundance of the $^{10}\text{B}$ isotope?
Answer: 20.0% Let the fractional abundance of $^{10}\text{B}$ be x. Then the fractional abundance of $^{11}\text{B}$ is (1-x). The relative atomic mass is the weighted average: $10.80 = (10 \times x) + (11 \times (1-x))$ . Solving for x: $10.80 = 10x + 11 - 11x$ ; $10.80 = 11 - x$ ; $x = 11 - 10.80 = 0.20$ . The percentage abundance is 0.20 × 100 = 20.0%.
When comparing the chemical reactions of propan-1-ol ( $\text{CH}_3\text{CH}_2\text{CH}_2\text{OH}$ ) and its deuterated isotopologue ( $\text{CH}_3\text{CH}_2\text{CH}_2\text{OD}$ ), which statement is most accurate? (D is the isotope $^{2}\text{H}$ )
Answer: The two compounds are expected to have nearly identical chemical properties as they have the same electron configuration. Isotopes have the same number of protons and electrons, leading to identical electron configurations. Since chemical reactions are governed by electron interactions, isotopes of an element exhibit virtually identical chemical properties. While there can be small differences in reaction rates (the kinetic isotope effect), for the purposes of IB Chemistry, their chemical behavior is considered the same. Both molecules are polar and would form the same oxidation products.
What is the total number of fundamental particles (protons, neutrons, and electrons) in one ion of $^{74}\text{Ge}^{4+}$ ? (Atomic number of Ge = 32)
Answer: 102 First, determine the number of each particle. Protons (p) = atomic number = 32. Neutrons (n) = mass number - atomic number = 74 - 32 = 42. Electrons (e) = number of protons - charge = 32 - 4 = 28. The total number of fundamental particles is the sum: p + n + e = 32 + 42 + 28 = 102.
Which property is expected to be significantly different between the isotopes uranium-235 and uranium-238?
Answer: The rate of diffusion of their gaseous hexafluoride compounds, $\text{UF}_6$ . Isotopes of an element have the same number of protons and electrons, resulting in identical electron configurations and thus nearly identical chemical properties (A, B, D). However, they have different numbers of neutrons and therefore different masses. Physical properties that depend on mass, such as density, boiling point, and rate of diffusion, will differ. According to Graham's Law of Effusion/Diffusion, the rate is inversely proportional to the square root of the molar mass. Since $^{235}\text{UF}_6$ and $^{238}\text{UF}_6$ have different masses, their rates of diffusion will be significantly different.
Consider two species, $^{A}_{Z}X$ and $^{B}_{Z+1}Y$ . If these two species have the same number of neutrons, what is the relationship between their mass numbers, A and B?
Answer: A = B - 1 The number of neutrons in a species is given by its mass number minus its atomic number. For species X: neutrons = A - Z. For species Y: neutrons = B - (Z+1) = B - Z - 1. If they have the same number of neutrons: A - Z = B - Z - 1. Adding Z to both sides: A = B - 1.
An isotope of element X has a mass number of 58 and contains 30 neutrons. An isotope of element Y has a mass number of 60 and contains 32 neutrons. What is the relationship between neutral atoms of X and Y?
Answer: They are isotopes of the same element. For element X: Atomic number (Z) = Mass number (A) - Number of neutrons (n) = 58 - 30 = 28. For element Y: Atomic number (Z) = 60 - 32 = 28. Since both X and Y have an atomic number of 28, they are both atoms of the element Nickel (Ni). Atoms with the same number of protons but different numbers of neutrons (and thus different mass numbers) are isotopes of the same element.
Two isotopes of the same element have mass numbers that differ by 4. If the lighter isotope has 18 neutrons and the heavier isotope has a neutron-to-proton ratio of 1.22, how many protons does this element have?
Answer: 18 protons Let the number of protons be P (same for both isotopes). Light isotope: mass number = P + 18. Heavy isotope: mass number = P + 18 + 4 = P + 22, and neutrons = 22. For the heavy isotope, neutron/proton ratio = 22/P = 1.22, so 22 = 1.22P, giving P = 22/1.22 = 18.03 ≈ 18. Check: light isotope has 18 protons + 18 neutrons = mass 36; heavy isotope has 18 protons + 22 neutrons = mass 40 (differs by 4 ✓). Neutron/proton ratio = 22/18 = 1.22 ✓.
An element exists as two naturally occurring isotopes. Isotope 1 has a mass of 62.930 u and accounts for 69.17% abundance. Isotope 2 has a mass of 64.928 u and accounts for 30.83% abundance. Based on this isotopic data, how many neutrons are present in the nucleus of the more abundant isotope?
Answer: 34 neutrons in the predominant nuclear isotope First, calculate the average atomic mass: (0.6917 × 62.930) + (0.3083 × 64.928) = 43.52 + 20.02 = 63.54 u. This corresponds to copper (Cu, atomic number 29). The more abundant isotope has mass ≈ 63 u (rounded from 62.930). Since atomic number = 29 protons, neutrons = mass number - protons = 63 - 29 = 34 neutrons.
An ion X³⁻ contains 50 neutrons and has a total of 36 electrons. In which group and period of the periodic table is element X found?
Answer: Group 15, Period 4 The ion has a 3- charge and 36 electrons. The neutral atom of X must have 36 - 3 = 33 electrons, and therefore 33 protons. The atomic number Z=33 identifies the element as Arsenic (As). The electron configuration of As is [Ar] 4s² 3d¹⁰ 4p³. The highest principal energy level (n) is 4, so it is in Period 4. As a p-block element, its group number is 10 + (number of valence s and p electrons) = 10 + (2 + 3) = 15. Thus, it is in Group 15, Period 4.

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