Structure of Atoms and Nuclei — MHT-CET Physics

Formulas (3)

• Radius, Speed and Everything Built From Them · Bohr orbit
  $$r_n \propto \frac{n^2}{Z}, \qquad v_n \propto \frac{Z}{n}, \qquad mvr = \frac{nh}{2\pi}$$
• Energy Levels and the Photon Between Them · Energy of the nth level
  $$E_n = -\frac{13.6\,Z^2}{n^2}\ \text{eV}, \qquad h\nu = E_i - E_f$$
• The Quantum Condition Outside the Atom · Rotor and charge in a field
  $$E_{\text{rot}} = \frac{n^2 h^2}{8\pi^2 I}, \qquad E_{B} = \frac{n\,qBh}{4\pi m}$$

Watch out for (5)

• Numbering the excited states from 1
  → Radius, Speed and Everything Built From Them
• Stopping at the current for the field at the nucleus
  → Radius, Speed and Everything Built From Them
• Saying the potential energy falls as the electron moves out
  → Energy Levels and the Photon Between Them
• Forgetting Z² when changing the atom
  → Energy Levels and the Photon Between Them
• Writing L = nh
  → The Quantum Condition Outside the Atom

Formulas (2)

• The Series, Their First Lines and Their Limits · Series limit
  $$\frac{1}{\lambda_\infty} = \frac{R}{n_f^2}, \qquad \nu_\infty = \frac{Rc}{n_f^2}$$
• Ratios of Two Lines · Rydberg formula
  $$\frac{1}{\lambda} = RZ^2\left(\frac{1}{n_f^2} - \frac{1}{n_i^2}\right)$$

Watch out for (4)

• Calling the series limit the longest wavelength
  → The Series, Their First Lines and Their Limits
• Using n_f = 1 for every series
  → The Series, Their First Lines and Their Limits
• Dividing wavelengths the way the brackets divide
  → Ratios of Two Lines
• Counting an upward jump as emission
  → Ratios of Two Lines

Formulas (3)

• The Decay Law and Half-Life · Decay law
  $$N = N_0 e^{-\lambda t}, \qquad T_{1/2} = \frac{\ln 2}{\lambda}, \qquad A = \lambda N$$
• Counting Alpha and Beta Decays · Counting decays
  $$n_\alpha = \frac{A_i - A_f}{4}, \qquad n_\beta = 2n_\alpha - (Z_i - Z_f)$$
• Binding Energy and a Nucleus That Splits · Binding energy
  $$BE = \left[Zm_p + (A - Z)m_n - M\right]c^2$$

Watch out for (6)

• Answering 'left' when the question asks 'decayed'
  → The Decay Law and Half-Life
• Multiplying N by T for activity
  → The Decay Law and Half-Life
• Pairing beta-plus with an antineutrino
  → Counting Alpha and Beta Decays
• Counting betas before alphas
  → Counting Alpha and Beta Decays
• Taking the radius ratio as the mass ratio
  → Binding Energy and a Nucleus That Splits
• Writing the binding energy with the nucleus first
  → Binding Energy and a Nucleus That Splits