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Questions and Answers
Which of the following was a weakness of the Articles of Confederation?
Which of the following was a weakness of the Articles of Confederation?
- No executive branch (correct)
- The power to regulate interstate trade
- The ability to declare peace
- A strong central government
The Articles of Confederation allowed the government to effectively regulate trade.
The Articles of Confederation allowed the government to effectively regulate trade.
False (B)
What was the main goal of the Northwest Ordinance?
What was the main goal of the Northwest Ordinance?
To establish a process for admitting new states to the United States.
The Northwest Ordinance required a population of ________ settlers for a territory to apply for statehood.
The Northwest Ordinance required a population of ________ settlers for a territory to apply for statehood.
The Great Compromise resolved the issue of representation in Congress by:
The Great Compromise resolved the issue of representation in Congress by:
The Great Compromise led to the creation of a unicameral Congress.
The Great Compromise led to the creation of a unicameral Congress.
What issue did the Three-Fifths Compromise address?
What issue did the Three-Fifths Compromise address?
According to the Three-Fifths Compromise, only __________ of the enslaved population could be counted towards representation and taxation.
According to the Three-Fifths Compromise, only __________ of the enslaved population could be counted towards representation and taxation.
Federalists supported the Constitution because they believed it would create:
Federalists supported the Constitution because they believed it would create:
Federalists favored giving more power to individual state governments.
Federalists favored giving more power to individual state governments.
What was the main concern of the Anti-Federalists regarding the Constitution?
What was the main concern of the Anti-Federalists regarding the Constitution?
The Anti-Federalists wanted a __________ to protect citizens' rights from the power of the central government.
The Anti-Federalists wanted a __________ to protect citizens' rights from the power of the central government.
The system of checks and balances is designed to:
The system of checks and balances is designed to:
Checks and balances ensure that each branch of government has exactly the same amount of power.
Checks and balances ensure that each branch of government has exactly the same amount of power.
Match each term to its correct description:
Match each term to its correct description:
Which of the following best describes the Anti-Federalists' position regarding the Constitution?
Which of the following best describes the Anti-Federalists' position regarding the Constitution?
The Federalist papers were written to argue against the ratification of the Constitution.
The Federalist papers were written to argue against the ratification of the Constitution.
What specific power did the Articles of Confederation lack that significantly hindered its effectiveness?
What specific power did the Articles of Confederation lack that significantly hindered its effectiveness?
The system of __________ ensures that no single branch of government can exert absolute control over the others.
The system of __________ ensures that no single branch of government can exert absolute control over the others.
Match the following individuals with their stance on the Constitution:
Match the following individuals with their stance on the Constitution:
Flashcards
Articles of Confederation
Articles of Confederation
America's first government, it was weak because it feared abuse of power and lacked an executive branch and the power to regulate trade.
Northwest Ordinance
Northwest Ordinance
A system for admitting new states to the U.S., requiring 60,000 settlers before a territory could govern itself.
Great Compromise
Great Compromise
Determined representation in Congress; both large and small states send representatives to a bicameral Congress.
Three-Fifths Compromise
Three-Fifths Compromise
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Federalist
Federalist
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Anti-Federalist
Anti-Federalist
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Checks and balances
Checks and balances
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Study Notes
- Quantum mechanics explains the behavior of matter and radiation at the atomic level
- Quantum mechanics aims to combine wave and particle properties into a single theory
Problems with Classical Mechanics
- Classical mechanics fails to explain many atomic phenomena
- Classical mechanics predicts unstable atoms
History of Quantum Mechanics
1900: Planck
- Addressed blackbody radiation.
- Energy equation: ( E = h\nu = \hbar \omega ), where ( \hbar = \frac{h}{2\pi} ).
1905: Einstein
- Explained the photoelectric effect.
- Postulated that light consists of discrete quanta (photons).
1913: Bohr
- Proposed a model of the hydrogen atom.
- Introduced the concept of quantized energy levels.
1923: de Broglie
- Introduced wave-particle duality.
- Equation: ( \lambda = \frac{h}{p} )
1925-1926: Schrödinger, Heisenberg, Born
- Established the field of quantum mechanics
Key Experiments in Quantum Mechanics
Double Slit Experiment
- Electrons fired at a screen with two slits still create an interference pattern, even when each electron passes through only one slit
- This demonstrates the wave-particle duality of matter
Stern-Gerlach Experiment
- Silver atoms fired through a magnetic field are deflected in two directions, corresponding to the two possible values of their spin.
- Illustrates the quantization of angular momentum
Principles of Quantum Mechanics
- The state of a system is described by a wave function ( \psi )
- Observables are represented by operators
- Possible outcomes of a measurement are the eigenvalues of the corresponding operator.
- The probability of measuring a particular eigenvalue is given by the square of the amplitude of the corresponding eigenstate in the wave function
- The time evolution of the wave function is governed by the Schrödinger equation: ( i\hbar \frac{\partial \psi}{\partial t} = \hat{H} \psi ), where ( \hat{H} ) is the Hamiltonian operator.
Simple Math in Quantum Mechanics
Complex Numbers
- ( z = a + bi = re^{i\theta} )
- ( i = \sqrt{-1} )
- ( r = \sqrt{a^2 + b^2} )
- ( \theta = \tan^{-1}(\frac{b}{a}) )
Linear Algebra
Vectors
- ( |v\rangle = \begin{pmatrix} v_1 \ v_2 \ \vdots \ v_n \end{pmatrix} )
Inner Product
- ( \langle u | v \rangle = \sum_{i=1}^{n} u_i^* v_i )
Matrices
- ( M = \begin{pmatrix} M_{11} & M_{12} & \cdots & M_{1n} \ M_{21} & M_{22} & \cdots & M_{2n} \ \vdots & \vdots & \ddots & \vdots \ M_{m1} & M_{m2} & \cdots & M_{mn} \end{pmatrix} )
Eigenvalues and Eigenvectors
- ( M |v\rangle = \lambda |v\rangle )
Summary of Quantum Mechanics
- Quantum mechanics combines wave and particle properties
- Essential for understanding atomic level behavior of matter and radiation
- Based on principles like wave functions, operators, and the Schrödinger equation
- Uses math like complex numbers and linear algebra
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