38 Questions
What is the constant represented by the symbol R?
Rydberg constant
What is the name of the series of lines observed in the infrared region of the spectrum?
Brackett series
What did Bohr's theory provide a link to?
Atomic spectra and Planck's constant
What is the assumption in Bohr's theory regarding angular momentum of the electron?
It is quantized
What is the name of the physicist who studied under Rutherford at the Victoria University in Manchester?
Niels Bohr
What is the concept introduced by Bohr in his model of the atom?
Electrons are in definite energy levels
What is the name of the theory that states energy is not continuous but discrete?
Planck's quantum theory
What is the shape of the orbits in Bohr's model of the atom?
Circular
What is the net charge of a cation?
Positive
What happens when a neutral atom loses one or more electrons?
It becomes a cation
What is the wavelength of radiation emitted for the electronic transition from infinite to stationary state of hydrogen atom?
Calculations required to determine the answer
What is the energy of the electron in the first orbit of a hydrogen atom?
Calculations required to determine the answer
What is the radius of Bohr's first orbit for a hydrogen atom?
0.529 Å
What is the net charge of an anion?
Negative
Who proposed elliptical orbits instead of circular orbits?
Arnold Sommerfeld
What is observed when atomic spectra lines are in the presence of an applied magnetic field?
The lines split into several lines
What is a limitation of the Sommerfeld theory?
It cannot give the correct number of lines observed in fine structure
Who suggested that all matter could exhibit wave-like properties?
Louis Victor de Broglie
What is the equation that expresses energy in terms of wave properties?
E = hv
What is the Heisenberg Uncertainty Principle related to?
The position and momentum of a particle
What is the significance of the constant 'h' in the equation λ = h/p?
It is a constant of proportionality
What is the relationship between the momentum and wavelength of a moving electron?
They are inversely proportional
What is the value of n in the Bohr model?
Only positive integers
What happens to the energy of an electron when it is in a particular orbit?
It remains constant
What is the name of the series of spectroscopic lines observed when an electron returns to the ground state?
Lyman series
What is the relationship between the energy of an electron and its distance from the nucleus?
The energy of the electron increases as it moves away from the nucleus
What is the term for the paths in which electrons move around the nucleus?
Orbits
What is the difference between a neutral atom and an ion?
A neutral atom has the same number of protons and electrons, while an ion has a different number
What is the name of the constant that appears in the equation for the energy of an electron in the Bohr model?
Rydberg's constant
What is the term for the definite energy associated with each stationary orbit?
Quantized energy
What is the value of Z* for oxygen, given that Z = 8 and σ = 3.45?
4.55
What is the electron configuration of nitrogen in the Slater's Rule Calculation?
1s2 2s2 2p3
What is the shielding constant experienced by a 2p electron in the nitrogen atom?
3.10
What is the value of σ for a 3d electron in the bromine atom?
21.15
What is the electron configuration of bromine in the Slater's Rule Calculation?
1s2 2s2 2p6 3s2 3p6 4s2 3d10 4p5
What is the value of Z* for nickel, given that Z = 28 and σ = 20.45?
7.55
What is the electron configuration of nickel in the Slater's Rule Calculation?
1s2 2s2 2p6 3s2 3p6 3d8 4s2
What is the shielding constant for a 4s electron in nickel?
23.95
Study Notes
Hydrogen Spectra
- The Rydberg formula describes the wavelengths of light emitted by hydrogen: ῡ = R (1/ni² - 1/nf²)
- The formula is used to calculate the wavelengths of spectral lines in different series (e.g. Lyman, Balmer, Paschen)
Bohr Model of the Atom
- Electrons exist in definite energy levels (quantized) and move between these levels, emitting or absorbing energy corresponding to specific frequencies
- The energy states of H atoms are quantized, and electrons jump between energy levels, emitting or absorbing energy
- Bohr's theory explains the atomic spectra and is linked to Planck's constant (h)
Bohr's Assumptions
- Electrons can have only specific (quantized) energy values
- The angular momentum of the electron must be quantized for each discrete orbit
Summary of Bohr Model
- Electrons move in specified paths (orbits or shells) around the nucleus
- As long as the electron is in a particular orbit, its energy is constant (stationary orbit or stationary shell)
- The principal quantum number (n) can take values 1, 2, 3, 4, etc.
- Each stationary orbit corresponds to a definite energy
Multielectron Atoms
- Neutral atoms have the same number of protons and electrons
- Ions are charged atoms (cations have more protons than electrons, anions have more electrons than protons)
Electrons in Orbit about the Nucleus
- Atomic Structure: Neutral atoms have the same number of protons and electrons
- Ion Formation: Neutral atoms can lose or gain electrons to become ions
Problems
- Wavenumber calculations for transitions from outer levels to level 2
- Radius of Bohr's first orbit for hydrogen atom and energy of the electron in the orbit
- Wavelength and energy of radiation emitted for electronic transitions from infinite to stationary state of hydrogen atom
Sommerfeld Theory (Bohr-Sommerfeld Theory)
- Arnold Sommerfeld proposed elliptical orbits instead of circular orbits
- Limitations: cannot explain fine structure, does not provide information on relativistic intensities of fine lines, and is contrary to the uncertainty principle
Wave-Particle Duality of Electron
- Louis Victor de Broglie suggested that all matter can exhibit wave-like properties
- Wave-particle duality of photon: E = hv = hc/λ
- Combining equations: λ = h/p (de Broglie wavelength)
Heisenberg Uncertainty Principle
- States that it is impossible to know both the momentum and position of a particle at the same time
- Critical for small particles like electrons
Slater's Rule Calculation
- Example calculations for oxygen and nickel atoms
- Calculating shielding constants (σ) for 2p and 3d electrons
This quiz covers the formula and equations related to the hydrogen spectra, including the Rydberg constant and wavelength of radiation.
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