Modern Physics - Revision of previous lecture

  • Recap of the previous lecture

  • Important concepts covered:

    • Quantum mechanics
    • Wave-particle duality
    • Photon
    • Photoelectric effect
    • Atomic spectrums

  • Today’s agenda

  • Overview of the topics to be covered:

    • Bohr’s model of the atom
    • Atomic structure
    • Radioactivity
    • Nuclear reactions

  • Bohr’s model of the atom

  • Key points:

    • Proposed by Niels Bohr in 1913
    • Explains the stability of atoms and atomic spectra
    • Electrons orbit the nucleus in discrete energy levels
    • Emit or absorb energy when transitioning between levels
    • Equations: E = -13.6/n^2 eV, v = R_H(1/n_1^2 - 1/n_2^2)

  • Atomic structure

  • Key points:

    • Protons, neutrons, and electrons
    • Protons and neutrons in the nucleus
    • Electrons in energy levels around the nucleus
    • Atomic number and mass number
    • Isotopes and ions

  • Radioactivity

  • Key points:

    • Discovered by Henri Becquerel in 1896
    • Types of radioactive decay: alpha, beta, gamma
    • Half-life and decay constant
    • Equations: N(t) = N_0 e^(-λt), N(t) = N_0/2^(t/T), λ = 0.693/T

  • Nuclear reactions

  • Key points:

    • Nuclear fission and fusion
    • Fission: splitting of a heavy nucleus into lighter nuclei
    • Fusion: combining of light nuclei to form a heavier nucleus
    • Mass-energy equivalence (Einstein’s equation)
    • Equations: E = mc^2, ΔE = Δm c^2

  • Example: Bohr’s model of the atom

  • Consider an electron transition from n = 3 to n = 2.

  • Find the energy change and the frequency of the emitted photon.

  • Solution:

    • Energy change: ΔE = -13.6(1/2^2 - 1/3^2) eV
    • Frequency: v = R_H(1/n_1^2 - 1/n_2^2)

  • Example: Atomic structure

  • Calculate the number of protons, neutrons, and electrons in ^56_26Fe.

  • Solution:

    • Number of protons: atomic number = 26
    • Number of neutrons: mass number - atomic number = 56 - 26
    • Number of electrons: same as number of protons

  • Example: Radioactivity

  • A sample of a radioactive substance has an initial activity of 640 Bq. The half-life of the substance is 10 days. Calculate the activity of the substance after 30 days.

  • Solution:

    • Decay constant: λ = 0.693 / T
    • Activity after 30 days: N(t) = N_0 e^(-λt)

  • Example: Nuclear reactions

  • Calculate the energy released in the fusion of two deuterium nuclei.

  • Given: mass of deuterium nucleus = 2.014 u

  • Solution:

    • Mass-energy equivalence: E = mc^2
    • Energy released: ΔE = Δm c^2

  • Recap of today’s lecture

  • Key topics covered:

    • Bohr’s model of the atom
    • Atomic structure
    • Radioactivity
    • Nuclear reactions

  • Important equations and examples

  • Next lecture: Special theory of relativity

  1. Bohr’s model of the atom
  • Proposed by Niels Bohr in 1913
  • Explains the stability of atoms and atomic spectra
  • Electrons orbit the nucleus in discrete energy levels
  • Emit or absorb energy when transitioning between levels
  • Equations: E = -13.6/n^2 eV, v = R_H(1/n_1^2 - 1/n_2^2)
  1. Atomic structure
  • Protons, neutrons, and electrons
  • Protons and neutrons in the nucleus
  • Electrons in energy levels around the nucleus
  • Atomic number and mass number
  • Isotopes and ions
  1. Radioactivity
  • Discovered by Henri Becquerel in 1896
  • Types of radioactive decay: alpha, beta, gamma
  • Half-life and decay constant
  • Equations: N(t) = N_0 e^(-λt), N(t) = N_0/2^(t/T), λ = 0.693/T
  1. Nuclear reactions
  • Nuclear fission and fusion
  • Fission: splitting of a heavy nucleus into lighter nuclei
  • Fusion: combining of light nuclei to form a heavier nucleus
  • Mass-energy equivalence (Einstein’s equation)
  • Equations: E = mc^2, ΔE = Δm c^2
  1. Example: Bohr’s model of the atom
  • Consider an electron transition from n = 3 to n = 2.
  • Find the energy change and the frequency of the emitted photon.
  • Solution:
    • Energy change: ΔE = -13.6(1/2^2 - 1/3^2) eV
    • Frequency: v = R_H(1/n_1^2 - 1/n_2^2)
  1. Example: Atomic structure
  • Calculate the number of protons, neutrons, and electrons in ^56_26Fe.
  • Solution:
    • Number of protons: atomic number = 26
    • Number of neutrons: mass number - atomic number = 56 - 26
    • Number of electrons: same as number of protons
  1. Example: Radioactivity
  • A sample of a radioactive substance has an initial activity of 640 Bq. The half-life of the substance is 10 days. Calculate the activity of the substance after 30 days.
  • Solution:
    • Decay constant: λ = 0.693 / T
    • Activity after 30 days: N(t) = N_0 e^(-λt)
  1. Example: Nuclear reactions
  • Calculate the energy released in the fusion of two deuterium nuclei.
  • Given: mass of deuterium nucleus = 2.014 u
  • Solution:
    • Mass-energy equivalence: E = mc^2
    • Energy released: ΔE = Δm c^2
  1. Recap of today’s lecture
  • Key topics covered:
    • Bohr’s model of the atom
    • Atomic structure
    • Radioactivity
    • Nuclear reactions
  • Important equations and examples
  1. Next lecture: Special theory of relativity ``
  1. Recap of today’s lecture
  • Key topics covered:
    • Bohr’s model of the atom
    • Atomic structure
    • Radioactivity
    • Nuclear reactions
  • Important equations and examples
  1. Next lecture: Special theory of relativity
  • Overview of the topic
  • Key points to be covered:
    • Einstein’s postulates
    • Time dilation
    • Length contraction
    • Mass-energy equivalence
    • Examples and applications
  1. Einstein’s postulates
  • First postulate: The laws of physics are the same in all inertial reference frames.
  • Second postulate: The speed of light in vacuum is constant for all observers, regardless of the motion of the light source or the observer.
  • Implications and consequences of these postulates.
  1. Time dilation
  • Definition of time dilation
  • Time dilation equation: Δt’ = Δt / √(1 - (v^2 / c^2))
  • Explanation and examples of time dilation in different scenarios
  • Twin paradox
  1. Length contraction
  • Definition of length contraction
  • Length contraction equation: L’ = L / √(1 - (v^2 / c^2))
  • Explanation and examples of length contraction in different scenarios
  1. Mass-energy equivalence
  • Einstein’s famous equation: E = mc^2
  • Mass-energy equivalence principle
  • Consequences and applications of the equation
  1. Example: Time dilation
  • A spaceship is traveling at 0.8c relative to Earth. Calculate the time experienced by the astronauts on board for a journey of 5 years according to Earth’s reference frame.
  • Solution:
    • Time dilation equation: Δt’ = Δt / √(1 - (v^2 / c^2))
  1. Example: Length contraction
  • A 2-meter-long rod is moving at 0.9c relative to an observer. Calculate the length of the rod as measured by the observer.
  • Solution:
    • Length contraction equation: L’ = L / √(1 - (v^2 / c^2))
  1. Example: Mass-energy equivalence
  • Calculate the energy equivalent of a mass of 0.5 kg.
  • Solution:
    • Einstein’s equation: E = mc^2
  1. Recap of today’s lecture
  • Key topics covered:
    • Special theory of relativity
    • Einstein’s postulates
    • Time dilation
    • Length contraction
    • Mass-energy equivalence
  • Important equations and examples `` Hope this helps! Remember to remove the comments before using the slides.