Practice Questions

An electron in a hydrogen atom makes a transition from $n=5$ to $n=2$. Analyze the transition and identify the name of the series and the region of the electromagnetic spectrum to which this spectral line belongs.

State the two main drawbacks of Rutherford's nuclear model of the atom.

Define mass number (A) and atomic number (Z).

Examine the following set of quantum numbers: $n=4, l=2, m_l=0, m_s=+1/2$. Identify the orbital to which this electron belongs.

Evaluate the possibility of an atomic orbital defined by the quantum numbers n=2, l=2, m_l=0. Justify your conclusion based on the rules governing quantum numbers.

A laser pointer used in a presentation emits green light with a wavelength of $520$ nm. Calculate the energy of one mole of photons of this green light. (Avogadro's number $N_A = 6.022 \times 10^{23} \text{ mol}^{-1}$)

Propose a reason based on the (n+l) rule for why the 4s orbital is filled before the 3d orbital when building up the electronic configuration of potassium.

Define an atomic orbital as per the quantum mechanical model of an atom.

Describe J.J. Thomson's model of the atom. What is another common name for this model?

Identify the sub-atomic particles discovered by (a) J.J. Thomson, (b) Goldstein (characterised by Rutherford), and (c) James Chadwick.

What is meant by the dual behaviour of matter?

An ion with a mass number of 56 has 3 units of positive charge and 30 neutrons. Analyze the composition of this ion and calculate the number of electrons it contains.

An element has an electronic configuration of $[Ar] 3d^5 4s^1$. Analyze this configuration to identify the element and its atomic number.

Calculate the wavelength of the radiation emitted when an electron in a $Li^{2+}$ ion transitions from the $n=4$ state to the $n=2$ state. (Rydberg constant for hydrogen $R_H = 109677 \text{ cm}^{-1}$)

The electronic configuration of Copper (Cu, Z=29) is an exception to the Aufbau principle. (a) Write the expected electronic configuration based on the Aufbau principle. (b) Write the actual, observed electronic configuration. (c) Analyze and explain in detail the two main reasons for the stability of the observed configuration over the expected one.

Justify why Bohr's model is inadequate for multi-electron atoms, citing a specific quantum mechanical principle or effect it fails to account for.

Critique the statement: "An electron in an atom follows a fixed, circular path called an orbit." Use Heisenberg's Uncertainty Principle in your argument.

Formulate a hypothesis to explain why the electronic configuration of Chromium (Cr) is [Ar] 3d^5 4s^1 instead of the expected [Ar] 3d^4 4s^2.

Propose a complete quantum mechanical description for an electron occupying a 3d orbital. Your proposal must: a) Identify all possible valid sets of the four quantum numbers (n, l, m_l, m_s). b) Describe the characteristic shape and spatial orientation of the five degenerate 3d orbitals. c) Evaluate and justify the number of angular and radial nodes present in a 3d orbital.

Compare the de Broglie wavelengths of a proton and an alpha particle if they are accelerated through the same potential difference.

Define the photoelectric effect and list two key observations from the experiment.

Summarize the main observations from Rutherford's alpha-particle scattering experiment.

What is black-body radiation?

When light of frequency $1.5 \times 10^{15}$ Hz strikes a metal surface, electrons are ejected with a kinetic energy of $5.0 \times 10^{-19}$ J. Calculate the work function ($W_0$) and the threshold frequency ($\nu_0$) of the metal.

Demonstrate that the circumference of the nth Bohr orbit for the hydrogen atom is an integral multiple of the de Broglie wavelength associated with the electron revolving in that orbit.

State the Heisenberg Uncertainty Principle.

List the four quantum numbers and name the property of an electron or orbital that each one describes.

Explain the key postulates of Bohr's model of the hydrogen atom.

What are isotopes and isobars? Provide one example for each.

Describe the shapes of s-orbitals and p-orbitals.

The speed of an electron is measured to be $5.0 \times 10^3$ m s$^{-1}$ with an uncertainty of $0.02\%$. Calculate the minimum uncertainty in determining the position of this electron. (Mass of electron $m_e = 9.1 \times 10^{-31}$ kg)

Critique the common misconception of an atomic orbital as a rigid container for an electron. Formulate a more scientifically accurate description using the concepts of the wave function (\psi) and probability density (|\psi|^2), and explain the significance of a 'node'.

Critique the aufbau principle by providing two examples of elements that are exceptions to its filling order. Formulate a detailed explanation for these exceptions based on the quantum mechanical concepts of symmetrical electron distribution and exchange energy. Support your justification with orbital diagrams.

Critique Rutherford's nuclear model of the atom. Propose three specific modifications, based on Maxwell's electromagnetic theory and observed atomic spectra, that were essential in the formulation of Bohr's model.

Justify the dual wave-particle nature of an electron using the de Broglie relation and the Davisson-Germer experiment. Then, evaluate which of the following will exhibit a more significant (i.e., measurable) wave character and justify your answer with calculations: a cricket ball (mass 150 g, velocity 30 m/s) or an electron (mass 9.1 \times 10^{-31} kg, velocity 1.6 \times 10^6 m/s).

Design a conceptual experiment to demonstrate the photoelectric effect. Propose how you would use this setup to determine the work function (W_0) and Planck's constant (h) for an unknown metal, and sketch the expected graph.

Derive the relationship between the circumference of the n^{th} Bohr orbit for a hydrogen atom and the de Broglie wavelength of the electron in that orbit. Justify how this result provides a physical basis for Bohr's postulate of angular momentum quantization.

Using the $(n+l)$ rule, analyze and arrange the following orbitals in order of increasing energy: $4d, 5p, 4f, 6s$. Justify your arrangement.

An electron in a hydrogen-like species transitions from an excited state n_i to a final state n_f = 2, emitting a photon with a wavelength of 486.1 nm. Formulate a method to identify both the species (by finding its atomic number Z) and the initial state n_i. Justify your steps and perform the identification.

Design a hypothetical one-electron species where the electron transition from n=3 to n=1 produces a photon with just enough energy to eject a photoelectron from a silver surface (Work function = 4.7 eV). Formulate the steps to calculate the atomic number (Z) of this species, and then perform the calculation to determine Z.

State the Aufbau principle, Pauli's exclusion principle, and Hund's rule of maximum multiplicity.

Evaluate the following two sets of quantum numbers, which describe the outermost electron in element A and element B, respectively. Justify which element would be expected to have a higher first ionization energy.

• Element A: n=3, l=0, m_l=0, m_s=+1/2
• Element B: n=2, l=1, m_l=+1, m_s=+1/2

Naturally occurring chlorine is a mixture of two isotopes: $^{35}Cl$ (isotopic mass $34.97$ u) and $^{37}Cl$ (isotopic mass $36.97$ u). If the average atomic mass of chlorine is $35.45$ u, calculate the percentage abundance of each isotope.

In a photoelectric effect experiment, irradiating a metal with light of wavelength $250$ nm produces photoelectrons with a maximum kinetic energy of $3.1$ eV. When the same metal is irradiated with light of wavelength $200$ nm, the maximum kinetic energy is $4.4$ eV. Using this data, calculate: (a) The value of Planck's constant. (b) The work function of the metal in eV.

The electron in a hydrogen atom undergoes a transition to the $n=2$ state, emitting radiation with a wavelength of $434$ nm. Analyze this transition to calculate: (a) The initial principal quantum number ($n_i$) from which the electron fell. (b) The energy of this initial state in Joules. (c) The radius of this initial Bohr orbit in picometers. ($R_H = 2.18 \times 10^{-18}$ J)