Section 1: Basic concepts and atomic structure

A sample of element E contains three isotopes with atomic masses $40.0\ \mathrm{u}$, $42.0\ \mathrm{u}$ and $44.0\ \mathrm{u}$. The lightest isotope makes up $70.0\%$ of the atoms, and the average atomic mass of E is $40.8\ \mathrm{u}$. What percentage of the atoms are the $44.0\ \mathrm{u}$ isotope?

A gaseous mixture of CH₄ and SO₂ has a vapour density of 20 (relative to hydrogen gas). What is the percentage by mass of SO₂ in the mixture? (H = 1, C = 12, O = 16, S = 32)

Read the following statements about the laws of chemical combination and atomic masses. (a) Equal volumes of N₂ and CO₂ at the same temperature and pressure contain equal numbers of molecules and so have equal masses. (b) When hydrogen and chlorine react to form hydrogen chloride, all three gases measured at the same temperature and pressure, the volumes of H₂, Cl₂ and HCl are in the ratio 1 : 1 : 2. (c) In CO and CO₂, the masses of oxygen that combine with 12 g of carbon are in the ratio 1 : 2. (d) One atomic mass unit is one-twelfth of the mass of one atom of carbon-12. (e) Dalton's atomic theory, as he stated it, explained Gay-Lussac's law of gaseous volumes. (f) Water made by burning hydrogen and water purified from a river both contain hydrogen and oxygen in the mass ratio 1 : 8 (H = 1, O = 16). How many of the statements above are correct?

In one experiment, $2.80\ \mathrm{g}$ of element Z combines with $1.60\ \mathrm{g}$ of oxygen to form oxide I, whose formula is Z₂O₃. In another, $4.20\ \mathrm{g}$ of Z combines with $4.00\ \mathrm{g}$ of oxygen to form oxide II. What is the formula of oxide II?

$50\ \mathrm{mL}$ of $0.20\ \mathrm{mol\,L^{-1}}$ BaCl₂ solution is mixed with $50\ \mathrm{mL}$ of $0.30\ \mathrm{mol\,L^{-1}}$ Na₂SO₄ solution, and BaSO₄ precipitates completely. Taking the volumes as additive, what is the concentration of sulphate ions left in the solution?

$2.4\ \mathrm{g}$ of magnesium is added to $150\ \mathrm{mL}$ of $1.0\ \mathrm{mol\,L^{-1}}$ HCl: Mg + 2HCl → MgCl₂ + H₂. All the hydrogen formed is passed over $12.0\ \mathrm{g}$ of heated CuO and reacts completely: CuO + H₂ → Cu + H₂O, the water leaving as vapour. What is the mass of the solid left? (H = 1, O = 16, Mg = 24, Cu = 64)

$28\ \mathrm{g}$ of N₂ and $9.0\ \mathrm{g}$ of H₂ are heated in a sealed vessel. Assume the reaction N₂ + 3H₂ → 2NH₃ goes to completion. Which statement is correct? (H = 1, N = 14)

A copper-containing protein has $0.16\%$ copper by mass, and each molecule contains two copper atoms. What is the molar mass of the protein? (Cu = 64)

Nitric acid is made from ammonia in three steps: 4NH₃ + 5O₂ → 4NO + 6H₂O, with an $80\%$ yield; 2NO + O₂ → 2NO₂, complete; and 3NO₂ + H₂O → 2HNO₃ + NO, complete, the NO formed in this step not being recycled. What mass of HNO₃ is obtained from $34\ \mathrm{kg}$ of NH₃? (H = 1, N = 14, O = 16)

Which sample contains the greatest total number of atoms? (H = 1, C = 12, O = 16, Ca = 40)

A yellow solid compound of phosphorus and sulphur contains $56.4\%$ phosphorus by mass. What is its empirical formula? (P = 31, S = 32)

Given below are two statements. Statement I: Equal volumes of O₂ and O₃, at the same temperature and pressure, contain equal numbers of oxygen atoms. Statement II: CO and CO₂ contain carbon and oxygen in different mass ratios, so they show that the law of definite proportions does not hold. Choose the correct answer.

Light of wavelength $155\ \mathrm{nm}$, and then light of wavelength $248\ \mathrm{nm}$, falls on a clean metal surface. The maximum speed of the photoelectrons ejected by the $155\ \mathrm{nm}$ light is twice their maximum speed with the $248\ \mathrm{nm}$ light. What is the threshold wavelength of the metal? (Take $hc$ $= 1240\ \mathrm{eV\,nm}$.)

A sample of a one-electron ion of unknown atomic number Z is excited so that its electrons all reach one particular level and none higher. On returning to the ground state, the sample emits exactly 10 distinct spectral lines, the most energetic of which has a photon energy of $326.4\ \mathrm{eV}$. How much energy is needed to remove the electron from the $n$ $= 3$ level of this ion? ($E_n$ $= -\frac{13.6\,Z^2}{n^2}\ \mathrm{eV}$)

A He⁺ ion makes the transition from $n$ $= 4$ to $n$ $= 2$. The photon emitted is absorbed by a hydrogen atom in its first excited state ($n$ $= 2$). What is the kinetic energy of the electron ejected from the hydrogen atom? (For a one-electron species, $E_n$ $= -\frac{13.6\,Z^2}{n^2}\ \mathrm{eV}$.)

Which electronic transition in the Li²⁺ ion (Z = 3) emits light of the same wavelength as the transition from n = 2 to n = 1 in a hydrogen atom?

For the hydrogen atom, what is the ratio of the longest wavelength in the Paschen series to the shortest wavelength in the Brackett series?

A proton and an alpha particle, each starting from rest, are accelerated through the same potential difference. Taking the mass of the alpha particle as 4 times that of the proton, what is the ratio of the de Broglie wavelength of the proton to that of the alpha particle?

Read the following statements about the Bohr model of one-electron species. (a) In a hydrogen atom, the energy gap between n = 2 and n = 3 is larger than that between n = 3 and n = 4. (b) The radius of the n = 2 orbit of He⁺ equals the radius of the n = 1 orbit of a hydrogen atom. (c) The ionisation energy of ground-state He⁺ is four times that of a ground-state hydrogen atom. (d) The speed of the electron in a Bohr orbit decreases as n increases. (e) The photon at the short-wavelength limit of the Lyman series of hydrogen has an energy of 13.6 eV. (f) The kinetic energy of the electron in a Bohr orbit is equal to its total energy. How many of the statements above are correct?

The maximum kinetic energy of photoelectrons is plotted against the frequency of the incident light for two metals P and Q. The work function of Q is greater than that of P. Which statement is correct?

In the Bohr model, the circumference of an allowed orbit holds a whole number of de Broglie wavelengths of the electron. What is the ratio of the de Broglie wavelength of the electron in the n = 3 orbit of He⁺ (Z = 2) to that in the n = 2 orbit of Li²⁺ (Z = 3)?

Light of wavelength $310\ \mathrm{nm}$ falls on a metal whose work function is $2.5\ \mathrm{eV}$. What is the de Broglie wavelength of the fastest photoelectrons? ($hc$ $= 1240\ \mathrm{eV\,nm}$, $h$ $= 6.6 \times 10^{-34}\ \mathrm{J\,s}$, $m_e$ $= 9.1 \times 10^{-31}\ \mathrm{kg}$, $1\ \mathrm{eV}$ $= 1.6 \times 10^{-19}\ \mathrm{J}$, $\sqrt{43.7}$ $= 6.61$)

Scandium (Z = 21) has one more electron than calcium (Z = 20). In the ground-state atoms, which set of quantum numbers could describe this extra electron of scandium?

Each line below gives a set of quantum numbers $(n, l, m_l, m_s)$ proposed for an electron in an atom. (a) $n$ $= 3,\ l$ $= 2,\ m_l$ $= -2,\ m_s$ $= +\frac{1}{2}$. (b) $n$ $= 2,\ l$ $= 2,\ m_l$ $= 0,\ m_s$ $= -\frac{1}{2}$. (c) $n$ $= 4,\ l$ $= 0,\ m_l$ $= 0,\ m_s$ $= -\frac{1}{2}$. (d) $n$ $= 4,\ l$ $= 3,\ m_l$ $= -3,\ m_s$ $= +\frac{1}{2}$. (e) $n$ $= 5,\ l$ $= 1,\ m_l$ $= 1,\ m_s$ $= 0$. (f) $n$ $= 3,\ l$ $= 1,\ m_l$ $= -1,\ m_s$ $= +\frac{1}{2}$. How many of these sets are allowed?

For a one-electron species of atomic number Z, the 2s wave function is $\psi_{2s} \propto \left(2 - \frac{Zr}{a_0}\right)e^{-Zr/2a_0}$, where $a_0$ $= 52.9\ \mathrm{pm}$. How far from the nucleus is the radial node of the 2s orbital of Li²⁺ (Z = 3)?

Which pair of gaseous species, each in its ground state, has the same number of unpaired electrons? (Z: V 23, Cr 24, Mn 25, Fe 26, Co 27, Ni 28)

How many of the following gaseous species, each in its ground state, have exactly four unpaired electrons? Fe, Cr, Cr²⁺, Mn³⁺, Mn⁺, Co³⁺, Ni, Co²⁺ (Z: Cr 24, Mn 25, Fe 26, Co 27, Ni 28)

Using the (n + l) rule, which order of increasing energy is correct for the 4f, 5d, 6s and 6p orbitals of a many-electron atom?

Read the following statements about electronic configurations of gaseous atoms and ions in their ground states. (Z: Cr 24, Mn 25, Fe 26, Cu 29) (a) Cr has the configuration [Ar]3d⁵4s¹; the half-filled 3d subshell gains extra exchange energy. (b) When Fe forms Fe²⁺, both electrons are removed from the 3d subshell. (c) Cu⁺ has a completely filled 3d subshell. (d) A 3d orbital has a lower value of n + l than a 4p orbital. (e) Mn²⁺ and Fe³⁺ have the same number of unpaired electrons. (f) Gaseous Zn²⁺ has no unpaired electrons. How many of the statements above are correct?

Read the following statements about atomic orbitals. (a) For the 2s orbital of a hydrogen atom, the wave function ψ changes sign at the radial node. (b) For the 1s orbital of a hydrogen atom, the probability density ψ² is greatest at the nucleus. (c) For the 1s orbital of a hydrogen atom, the radial probability of finding the electron, in a thin shell at distance r, is greatest at the nucleus. (d) A 3p orbital has one radial node. (e) In a hydrogen atom, the 3s and 3d orbitals have the same energy. (f) In a many-electron atom, the 3s and 3d orbitals have the same energy. How many of the statements above are correct?