Structure of Atom — MHT-CET Chemistry

Formulas (3)

• Counting protons, neutrons and electrons in a species · Electron count of a species
  $$e^- = Z - (\text{charge}) \qquad N = A - Z$$
• Identifying isoelectronic species by counting electrons · Isoelectronic test
  $$e^-_1 = Z_1 - q_1 \;\overset{?}{=}\; Z_2 - q_2 = e^-_2$$
• Average atomic mass and isotope abundance ratio · Weighted average atomic mass
  $$\bar{m} = \frac{m_1 x + m_2 (100 - x)}{100}$$

Reference tables (3)

Watch out for (12)

• Mass number counts nucleons, not electrons
  → The three subatomic particles and the nuclide notation
• Read the notation the right way up
  → The three subatomic particles and the nuclide notation
• A neutral atom of Ca has 20 electrons, but Ca-based ions do not
  → Counting protons, neutrons and electrons in a species
• Add for negative, subtract for positive
  → Counting protons, neutrons and electrons in a species
• 'Isotopes have equal neutrons' is FALSE
  → Isotopes, isobars, isotones and isoelectronic species
• Isotones vs isobars vs isotopes
  → Isotopes, isobars, isotones and isoelectronic species
• The neutral atom hidden among its ions
  → Identifying isoelectronic species by counting electrons
• Same electrons, not same protons
  → Identifying isoelectronic species by counting electrons
• Weight by abundance, don't just average
  → Average atomic mass and isotope abundance ratio
• Match the ratio order to the isotopes
  → Average atomic mass and isotope abundance ratio
• Hydrogen-like means one electron, not 'near hydrogen'
  → Isotope counts, hydrogen-like species and radioactivity
• Argon is the stable one
  → Isotope counts, hydrogen-like species and radioactivity

Formulas (3)

• Wave characteristics — wavelength, frequency, wavenumber, amplitude · Wavenumber
  $$\bar{\nu} = \dfrac{1}{\lambda}$$
• Speed of light relation, c = nu*lambda · Speed of light relation
  $$c = \nu\lambda \qquad \Rightarrow \qquad \nu = \dfrac{c}{\lambda}$$
• Planck's quantum theory and photon energy, E = h*nu = hc/lambda · Photon energy (Planck)
  $$E = h\nu = \dfrac{hc}{\lambda} \qquad (\text{per mole: } E \times N_A)$$

Reference tables (1)

Watch out for (9)

• Frequency vs wavelength — read the wording
  → Wave characteristics — wavelength, frequency, wavenumber, amplitude
• Match the wavenumber unit to lambda
  → Wave characteristics — wavelength, frequency, wavenumber, amplitude
• Convert nm to metres before dividing
  → Speed of light relation, c = nu*lambda
• c is the same for every EM radiation
  → Speed of light relation, c = nu*lambda
• Energy goes as 1/lambda, not lambda
  → Planck's quantum theory and photon energy, E = h*nu = hc/lambda
• Per photon vs per mole
  → Planck's quantum theory and photon energy, E = h*nu = hc/lambda
• Amplitude does not set energy
  → Planck's quantum theory and photon energy, E = h*nu = hc/lambda
• Long wavelength = LOW energy
  → The electromagnetic spectrum — order by frequency and energy
• VIBGYOR direction
  → The electromagnetic spectrum — order by frequency and energy

Formulas (6)

• Postulates and quantized angular momentum · Quantized angular momentum
  $$L = mvr = \dfrac{nh}{2\pi}$$
• Radius of the nth orbit · Radius of nth orbit
  $$r_n = 0.529\,\dfrac{n^2}{Z}\ \text{\AA}$$
• Energy of the nth orbit · Energy of nth orbit
  $$E_n = -2.18 \times 10^{-18}\,\dfrac{Z^2}{n^2}\ \text{J} = -13.6\,\dfrac{Z^2}{n^2}\ \text{eV}$$
• Velocity of the electron in the nth orbit · Velocity of electron in nth orbit
  $$v_n = 2.18 \times 10^{6}\,\dfrac{Z}{n}\ \text{m s}^{-1}$$
• Energy difference between levels and ionization energy · Energy gap between two orbits
  $$\Delta E = 13.6\,Z^2\left(\dfrac{1}{n_1^2} - \dfrac{1}{n_2^2}\right)\ \text{eV}$$
• Hydrogen-like species and limitations of the model · Test for a hydrogen-like species
  $$\text{electrons} = Z - (\text{charge}) = 1$$

Reference tables (1)

Watch out for (15)

• Rutherford placed the electrons OUTSIDE the nucleus
  → Rutherford's nuclear model and its drawbacks
• The stability failure is a CLASSICAL-physics problem
  → Rutherford's nuclear model and its drawbacks
• It is n h / 2 pi, not 2 pi n / h
  → Postulates and quantized angular momentum
• Angular momentum ignores Z
  → Postulates and quantized angular momentum
• Divide by Z for ions
  → Radius of the nth orbit
• Angstrom vs pm
  → Radius of the nth orbit
• Keep the minus sign
  → Energy of the nth orbit
• Z is squared, n is squared
  → Energy of the nth orbit
• Velocity goes as 1/n, not 1/n squared
  → Velocity of the electron in the nth orbit
• Higher Z, faster electron
  → Velocity of the electron in the nth orbit
• Ionization energy is positive
  → Energy difference between levels and ionization energy
• Bigger n subtracted from smaller n
  → Energy difference between levels and ionization energy
• Bohr formulas are single-electron only
  → Hydrogen-like species and limitations of the model
• Bohr explains hydrogen, not the Zeeman effect
  → Hydrogen-like species and limitations of the model
• Rutherford vs Bohr on electron energy
  → Hydrogen-like species and limitations of the model

Formulas (2)

• Rydberg equation — wavenumber of a spectral line · Rydberg equation
  $$\bar{\nu} = \dfrac{1}{\lambda} = R_H\, Z^2\left(\dfrac{1}{n_1^2} - \dfrac{1}{n_2^2}\right) \qquad (n_1 < n_2)$$
• Longest wavelength, series limit, and number of spectral lines · Number of spectral lines from orbit n
  $$\text{No. of lines} = \dfrac{n(n-1)}{2}$$

Reference tables (1)

Watch out for (6)

• n1 is the smaller orbit — keep the bracket positive
  → Rydberg equation — wavenumber of a spectral line
• Wavenumber and wavelength are reciprocals
  → Rydberg equation — wavenumber of a spectral line
• Balmer is visible, Lyman is not
  → The spectral series of hydrogen
• The series is named by the LOWER orbit, not the upper one
  → The spectral series of hydrogen
• Longest wavelength = smallest gap, not the biggest jump
  → Longest wavelength, series limit, and number of spectral lines
• n(n-1)/2 counts every downward jump
  → Longest wavelength, series limit, and number of spectral lines

Formulas (3)

• de Broglie wavelength — wave-particle duality · de Broglie wavelength and momentum
  $$\lambda = \dfrac{h}{mv} = \dfrac{h}{p} \qquad p = \dfrac{h}{\lambda}$$
• Heisenberg's uncertainty principle · Heisenberg uncertainty relation
  $$\Delta x \cdot \Delta p \geq \dfrac{h}{4\pi} \qquad \Delta x \cdot \Delta v \geq \dfrac{h}{4\pi m}$$
• Shell capacity, orbital energy order and nodes · Shell capacity, subshell capacity and nodes
  $$\text{orbitals} = n^2,\quad e^- _{\max} = 2n^2,\quad e^-_{\text{subshell}} = 2(2l+1) \qquad \text{nodes} = n-1,\ \text{radial} = n-l-1$$

Reference tables (2)

Watch out for (9)

• Divide by momentum, not by mass alone
  → de Broglie wavelength — wave-particle duality
• Convert Ångström to metres
  → de Broglie wavelength — wave-particle duality
• It is a fundamental limit, not an instrument error
  → Heisenberg's uncertainty principle
• Don't confuse it with Pauli or Aufbau
  → Heisenberg's uncertainty principle
• l ranges from 0 to n-1
  → The four quantum numbers
• m_l ranges from -l to +l
  → The four quantum numbers
• d(z2) is the shape exception
  → Orbital shapes from l
• Break an (n+l) tie with the smaller n
  → Shell capacity, orbital energy order and nodes
• Degeneracy of 2s and 2p is a hydrogen-only fact
  → Shell capacity, orbital energy order and nodes

Formulas (2)

• Ground-state configurations and the half-filled/fully-filled anomaly · The stable-subshell anomaly (Cr, Cu)
  $$\text{Cr}: [\text{Ar}]\,4s^1 3d^5 \qquad \text{Cu}: [\text{Ar}]\,4s^1 3d^{10}$$
• Counting unpaired electrons · Unpaired electrons in a subshell
  $$\text{unpaired} = \begin{cases} k, & k \le N \\ 2N - k, & k > N \end{cases}$$

Reference tables (1)

Watch out for (6)

• Pauli is about four quantum numbers, not position
  → The three orbital-filling rules
• Hund means all singly first, then pair
  → The three orbital-filling rules
• Chromium is 3d⁵4s¹, not 3d⁴4s²
  → Ground-state configurations and the half-filled/fully-filled anomaly
• Copper's 4s is singly occupied
  → Ground-state configurations and the half-filled/fully-filled anomaly
• Half-filled subshells hold the most unpaired electrons
  → Counting unpaired electrons
• Fully-filled means zero unpaired
  → Counting unpaired electrons