4 questions, one for each idea where we can. Answer them, then see which ideas to fix.
Question 1 of 4
An ion has a charge of 1−, contains 18 electrons and has a mass number of 37. How many neutrons are in its nucleus?
Answer and reasoning
A17 A student who thinks a nucleus has equal numbers of protons and neutrons picks this, after finding 17 protons. The number of neutrons is the mass number minus the number of protons: 37 − 17 = 20.
B18 A student who reads the 1− charge as one electron lost picks this, giving the nucleus 19 protons and 37 − 19 = 18 neutrons. A negative ion has one more electron than protons, so there are 17 protons.
C19 A student who takes the number of protons to equal the number of electrons picks this: 37 − 18 = 19. The ion has a 1− charge, so it has one fewer proton than electrons, 17.
D20Correct The ion has one more electron than protons, so it has 18 − 1 = 17 protons. The mass number is the number of protons plus neutrons, so there are 37 − 17 = 20 neutrons.
Working Charge = protons − electrons, so protons = 18 − 1 = 17. Neutrons = mass number − protons = 37 − 17 = 20.
Two particles with charges of +2 and −2 are separated by a distance d and attract each other with a force of magnitude F. Two other particles, with charges of +2 and −1, are separated by a distance of d/2. What is the magnitude of the force between the second pair of particles?
Answer and reasoning
A0.50F A student who thinks the charges alone decide the force picks this: the product of the charges is halved. The distance is also halved, which multiplies the force by 4, giving 2.00F.
B1.00F A student who takes the force to be inversely proportional to the distance picks this: (1/2) × 2 = 1. The force depends on 1/r², so halving the distance multiplies it by 4, not 2.
C2.00FCorrect The product of the charges is halved (4 to 2) and the distance is halved, which multiplies 1/r² by 4. The force is (1/2)(4)F = 2.00F.
D4.00F A student who thinks only the separation decides the force picks this: halving the distance multiplies the force by 4. The product of the charges is also halved, giving 2.00F.
Working F ∝ q₁q₂/r². The product of the charges changes from 4 to 2, a factor of 1/2. The distance is halved, so 1/r² increases by a factor of 4. New force = (1/2)(4)F = 2.00F.
The diagram shows a shell model of a neutral atom in its ground state. How many core electrons and how many valence electrons does the atom have?
Answer and reasoning
ACore 10, valence 5Correct The valence electrons are the 5 electrons in the outermost occupied shell. The core electrons are the electrons in the shells inside it: 2 + 8 = 10.
BCore 2, valence 13 A student who thinks core electrons are only those in the innermost shell picks this. The eight electrons in the second shell are also inner electrons, so there are 10 core electrons.
CCore 12, valence 3 A student who thinks valence electrons are only those in the last-filled subshell (3p³) picks this. The two 3s electrons are also in the outermost shell, so there are 5 valence electrons and 10 core electrons.
DCore 10, valence 3 A student who takes the number of valence electrons to be the number needed to fill the outer shell (8 − 5 = 3) picks this. Valence electrons are the outer electrons the atom has: 5.
Working The outermost occupied shell holds 5 electrons, so there are 5 valence electrons. The two inner shells hold 2 + 8 = 10 core electrons. Total 15, equal to the nuclear charge.
A ground-state aluminum atom has the electron configuration 1s²2s²2p⁶3s²3p¹. How does the energy required to remove a 2p electron from the atom compare with the energy required to remove the 3p electron?
Answer and reasoning
AIt is the same for both, since one nucleus attracts each of its electrons with equal force. A student who thinks a nucleus attracts all of its electrons equally picks this. The attraction depends on each electron's distance from the nucleus and on the electrons that shield it, and both differ for 2p and 3p.
BIt is greater for the 3p electron, as an electron in a higher energy level needs more energy to leave. A student who confuses the energy of an electron with the energy needed to remove it picks this. An electron in a higher energy level is held less strongly, so less energy is required to remove it.
CIt is smaller for a 2p electron, since six 2p electrons share an attraction that 3p has alone. A student who thinks the attraction of the nucleus is shared out among the electrons of a subshell picks this. The force on each electron is given by Coulomb's law and is not divided; the 2p electrons are closer and less shielded, so each is held more strongly.
DIt is greater for a 2p electron, which is closer to the nucleus and shielded by fewer electrons.Correct A 2p electron is in the second shell, closer to the nucleus than the 3p electron, and only the two 1s electrons lie inside it. By Coulomb's law it is attracted more strongly, so more energy is required to remove it.
In preparation: 0 of 4 sections compiled and reviewed. The rest show key terms and common mistakes from our question bank until they are.
1.5.A.1 Nucleus Fix
Nucleus
The small, positively charged center of an atom, made of protons and neutrons. It contains nearly all of the atom's mass.
Proton, neutron and electron
The particles that make up an atom. A proton has a charge of 1+ and a neutron has no charge; both are in the nucleus. An electron has a charge of 1− and is outside the nucleus. The number of protons identifies the element.
Ion
An atom or group of atoms with a net charge because its numbers of protons and electrons differ. A monatomic cation has fewer electrons than protons; a monatomic anion has more electrons than protons. The nucleus is unchanged when an ion forms.
Students often think The number of protons always equals the number of electrons, so the number of electrons in an ion gives its atomic number. In fact No. Only a neutral atom has equal numbers. An ion with a charge of 1− has one more electron than protons, so an ion with 18 electrons and a 1− charge has 17 protons.
Students often think A plus sign means something was added and a minus sign means something was removed, so a 2+ ion has gained two electrons and a 1− ion has lost one. In fact No. Electrons are negatively charged, so an atom that loses electrons becomes a positive ion and an atom that gains electrons becomes a negative ion.
1.5.A.2 Coulomb's law Fix
Coulomb's law
The relationship Fcoulombic ∝ q₁q₂/r²: the force between two charged particles is proportional to the product of their charges and inversely proportional to the square of the distance between them. Opposite charges attract and like charges repel.
Students often think Coulombic force is inversely proportional to the distance, so doubling the distance halves the force and halving the distance doubles it. In fact No. The force is inversely proportional to the square of the distance, so doubling the distance reduces the force to one-quarter.
Students often think The size of the charges alone decides how strongly two particles attract; the distance between them does not need to be considered. In fact No. The force depends on the product of the charges and on the distance between the particles: F ∝ q₁q₂/r².
1.5.A.3 Shell (energy level) Fix
Shell (energy level)
A group of electrons in an atom or ion with similar energies and similar average distances from the nucleus, labeled 1, 2, 3 and so on outward from the nucleus.
Subshell (sublevel)
A division of a shell, labeled by the shell number and a letter (1s, 2p, 3d). An s subshell holds up to 2 electrons, a p subshell up to 6, a d subshell up to 10 and an f subshell up to 14.
Ground-state electron configuration
The list of occupied subshells of an atom or ion in its lowest-energy state, with the number of electrons in each written as a superscript, for example 1s²2s²2p⁶3s¹ for sodium.
Aufbau principle
The principle that the ground-state configuration of an atom is built up by placing electrons in the lowest-energy subshells available. The filling order is read from the periodic table: 1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p, 5s, 4d, 5p.
Core electrons
The inner electrons of an atom. In a main-group element they are the electrons in the shells below the outermost occupied shell.
Valence electrons
The outer electrons of an atom. In a main-group element they are the electrons in the outermost occupied shell, in its s and p subshells.
Students often think Core electrons are only the two electrons in the innermost shell; every other electron is a valence electron. In fact No. The core electrons of a main-group atom are all of the electrons in the shells below its outermost occupied shell. A phosphorus atom (2, 8, 5) has 10 core electrons.
Students often think The valence electrons are only the electrons in the subshell written last in the configuration, so the s electrons of the outer shell are core electrons. In fact No. The valence electrons of a main-group atom are all of the electrons in its outermost occupied shell, in both the s and the p subshell. Phosphorus, …3s²3p³, has 5 valence electrons.
1.5.A.4 Ionization energy Fix
Ionization energy
The energy required to remove an electron from an atom or ion in the gas phase. Its relative size can be estimated qualitatively with Coulomb's law from the electron's distance from the nucleus and the effective charge attracting it.
Shielding and effective nuclear charge
Electrons that lie between the nucleus and an outer electron repel that electron and so reduce the net attraction it experiences; this is shielding. The effective nuclear charge is the net positive charge that the electron experiences as a result.
Students often think All the electrons of an atom are attracted equally because they are attracted by the same nucleus, so they need the same energy to remove. In fact No. An electron closer to the nucleus, with fewer electrons shielding it, is attracted more strongly than an outer electron of the same atom.
Students often think Atoms hold or give up electrons in order to have filled shells, so counting the electrons in a shell and the number needed to fill it tells how strongly an electron is held. In fact No. It is decided by the Coulombic attraction between the electron and the nucleus, which depends on the electron's distance from the nucleus and the effective charge attracting it.
7 more questions. Every wrong answer here is a real mistake students make, and you see why it is wrong as soon as you answer.
Question 1 of 7
The table gives the charges and the separation of the two particles in each of four pairs of oppositely charged particles. In which pair is the force of attraction between the two particles the greatest?
Answer and reasoning
APair 1Correct The force is proportional to q₁q₂/r². For this pair, 3/(150)² is 1.33 times the value for the +1 and −1 pair at 100 pm, and it is greater than the values for the other two pairs (0.56 and 0.96 on the same scale).
BPair 2 A student who thinks only the separation decides the force picks this pair, which has the smallest separation. Its charge product is only 1; the +3 and −1 pair at 150 pm has three times the charge product at 1.5 times the separation, giving 3/2.25 = 1.33 times the force.
CPair 3 A student who thinks the charges alone decide the force picks this pair, which has the largest charge product, 9. At 400 pm, 1/r² is one-sixteenth of its value at 100 pm, so the force is only 9/16 = 0.56 on the scale where the +1 and −1 pair is 1.00.
DPair 4 A student who takes the force to be inversely proportional to the distance picks this pair, for which q₁q₂/r = 6/250 is the largest. With 1/r², its value is 6/6.25 = 0.96, less than 1.33 for the +3 and −1 pair at 150 pm.
Working F ∝ q₁q₂/r². Relative values of q₁q₂/r² (× 10⁴ pm⁻²): +3 and −1 at 150 pm: 3/2.25 = 1.33; +1 and −1 at 100 pm: 1/1.00 = 1.00; +3 and −3 at 400 pm: 9/16.0 = 0.56; +3 and −2 at 250 pm: 6/6.25 = 0.96. The greatest is the pair with charges +3 and −1 at 150 pm.
The graph shows how the magnitude of the force between two oppositely charged particles depends on their separation. Based on the relationship shown by the graph, what is the magnitude of the force between the particles when their separation is 800 pm?
Answer and reasoning
A0.00 units A student who thinks charged particles attract only within a limited range picks this, because the curve has almost reached the axis. The force keeps decreasing as 1/r² and is small but not zero: 1.0/4 = 0.25 units.
B0.25 unitsCorrect The marked points show that the force falls to one-quarter each time the separation doubles (16.0, 4.0, 1.0), so F ∝ 1/r². Doubling the separation from 400 pm to 800 pm gives 1.0/4 = 0.25 units.
C0.50 units A student who takes the force to be inversely proportional to the separation picks this, halving the value at 400 pm. The marked points show the force falling to one-quarter, not one-half, when the separation doubles.
D1.00 units A student who reads the flat part of the curve as a constant value picks this. The curve only looks flat on this scale; the force continues to fall as 1/r², to 0.25 units at 800 pm.
Working The marked points show that each doubling of the separation divides the force by 4 (16.0 → 4.0 → 1.0), as F ∝ 1/r². From 400 pm to 800 pm the separation doubles again, so F = 1.0/4 = 0.25 units.
A ground-state iron atom has the electron configuration [Ar]4s²3d⁶. Which statement describes how a ground-state Fe²⁺ ion differs from the atom and gives its electron configuration?
Answer and reasoning
ATwo electrons have been removed from the 3d subshell, giving [Ar]4s²3d⁴. A student who thinks electrons are removed in the reverse of the filling order picks this. The 4s electrons, not the 3d electrons, are removed first; the ground-state ion has no 4s electrons.
BTwo electrons have been added to the 3d subshell, giving [Ar]4s²3d⁸. A student who reads the 2+ charge as two electrons gained picks this. A positive ion has fewer electrons than protons, so Fe²⁺ has 24 electrons, not 28.
CTwo protons have been added to the nucleus; [Ar]4s²3d⁶ is left unchanged. A student who thinks a positive ion forms by gaining protons picks this. The nucleus of iron keeps its 26 protons; the ion forms by losing two electrons, so the configuration changes to [Ar]3d⁶.
DTwo electrons have been removed from the 4s subshell, giving [Ar]3d⁶.Correct A 2+ ion has two fewer electrons than the atom. In the cations of the period 4 transition metals the 4s electrons are removed before any 3d electrons, so Fe²⁺ is [Ar]3d⁶.
A student writes the electron configuration 1s²2s²2p⁶3s²3p⁶3d³ for a ground-state scandium atom, which has 21 electrons. Which statement correctly evaluates the student's configuration?
Answer and reasoning
AIt is the ground state: subshells fill in order of shell number, so 3d is filled before 4s. A student who thinks every subshell of one shell fills before the next shell begins picks this. The periodic table shows that 4s is filled (K, Ca) before 3d begins at Sc, so the ground state is …4s²3d¹.
BIt is not the ground state: the third shell is full with 8 electrons, so the last three are 4s²4p¹. A student who takes the '2, 8, 8' pattern as the capacities of the shells picks this. The third shell has a 3d subshell and can hold 18 electrons; after 4s the next electron enters 3d, not 4p.
CIt is not the ground state: 4s fills before 3d, so the last three electrons are 4s²3d¹.Correct Scandium is the first element of the d block in period 4. After 3p the 4s subshell is filled (K, Ca), and the 21st electron enters 3d, giving 1s²2s²2p⁶3s²3p⁶4s²3d¹.
DIt is not the ground state: d subshells begin in the fourth shell, so the last three are 4s²4d¹. A student who gives every subshell filled in period 4 the shell number 4 picks this. The d subshell filled in period 4 is 3d; 4d is filled in period 5.
The table gives the energy required to remove the electron from each of three species. Each species has one electron, in the 1s subshell. Which statement is supported by the data and by Coulomb's law?
Answer and reasoning
AThe energy rises faster than the nuclear charge, because a greater charge also pulls the electron closer.Correct From +1 to +2 to +3 the energy rises by factors of 4.0 and 9.0 (1.31, 5.25, 11.8 MJ/mol), faster than the nuclear charge. With no other electrons present only the nucleus differs: by Coulomb's law a greater nuclear charge increases the attraction directly and also pulls the 1s electron closer, which increases the attraction further.
BThe energy rises in step with the nuclear charge, because the charges alone decide the attraction. A student who thinks the charges alone decide the attraction picks this, expecting the energy to double and triple. The table shows factors of 4.0 and 9.0: the electron is also closer to a nucleus of greater charge, and the distance matters as well.
CThe energy rises faster than the nuclear charge, because the charge of an ion adds to that of its nucleus. A student who treats the charge of an ion as an additional source of attraction picks this. The charge of He⁺ or Li²⁺ is simply the nuclear charge minus the charge of the one electron; the only attraction on the electron is that of the nucleus.
DThe energy rises in step with the nuclear charge, because the 1s electrons are equally far from each nucleus. A student who thinks electrons in the same subshell differ only in the number of protons attracting them picks this, expecting the energy to double and triple. The table shows factors of 4.0 and 9.0: a 1s electron is closer to a nucleus of greater charge, so the distance changes as well as the charge.
A student hypothesizes that, for electrons in the same subshell with the same shielding, a greater nuclear charge means that more energy is required to remove an electron. Which set of measurements would provide the best test of the hypothesis?
Answer and reasoning
AThe energy required to remove the outermost electron from each of Li, Na and K atoms A student who thinks nuclear charge is the only difference between these atoms picks this. The outermost electrons are in 2s, 3s and 4s, so the distance from the nucleus and the shielding change along with the nuclear charge, and the test is not controlled.
BThe energy required to remove an outermost electron from each of Ne, Na⁺ and Mg²⁺Correct Each species has the configuration 1s²2s²2p⁶, so in each case a 2p electron with the same shielding is removed, while the nuclear charge changes from +10 to +11 to +12. Only the variable in the hypothesis changes.
CThe energy required to remove the single electron from each of ¹H, ²H and ³H atoms A student who links the attraction of a nucleus to its mass picks this. The three isotopes have the same nuclear charge, +1, so these measurements do not vary the nuclear charge.
DThe energy required to remove an electron from each of Li, Li⁺ and Li²⁺ A student who takes the charge of an ion to be the charge of its nucleus picks this. All three species have a nuclear charge of +3; what changes is the number of electrons and the subshell from which the electron is removed.
A student wants to use Coulomb's law to predict whether more energy is required to remove a 1s electron from a carbon atom or from an oxygen atom. Which information does the student need?
Answer and reasoning
AThe mass of each nucleus and the mass of the electron that is removed from that atom A student who thinks a nucleus attracts electrons because of its mass picks this. Coulomb's law contains charges and distance, not masses.
BThe charge of each nucleus and the total number of electrons sharing its attraction A student who thinks a nucleus has a fixed amount of attraction that is shared among its electrons picks this. The force on an electron is not divided among the electrons; the distance of the 1s electron from the nucleus is needed instead.
CThe charge of each nucleus and the distance of the electron from that nucleusCorrect Coulomb's law relates the attraction to the charges and the distance between them. A 1s electron has no inner shells shielding it, so the charge of each nucleus (+6, +8) and the distance of the 1s electron from it are what the comparison needs.
DThe number of electrons in the outer shell of each atom and the number needed to fill it A student who explains how strongly electrons are held by how close an atom is to a filled shell picks this. The attraction for a 1s electron depends on the nuclear charge and the electron's distance from the nucleus.
Working Fcoulombic ∝ q₁q₂/r². The electron's charge is the same in both atoms, so the quantities needed are the charge attracting the 1s electron in each atom (the nuclear charge, +6 and +8; a 1s electron has no electrons in shells inside it) and the distance r of the 1s electron from each nucleus.
Compiled from the AP Chemistry Course and Exam Description (effective Fall 2024) and our question bank · Specialist review in progress. How these pages are made · Free, no account
