Questions and Answers
What happens to the energy of an electron as it gets closer to the nucleus?
The energy of an electron in a hydrogen atom is always positive.
False
What is the energy of an electron associated with the stationary state of Principal Quantum number = n = ∞ called?
Ionized hydrogen atom
The most negative energy value is given by n = ___, which corresponds to the most stable orbit.
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Match the following energy transitions with the correct phenomenon:
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What is the energy gap between two orbits given by?
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The energy of an electron is lowered when it is attracted by the nucleus.
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Why does the energy of an electron have a negative sign in equation (2.13)?
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What was characterised in 1919?
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The mass of a neutron is slightly less than that of a proton.
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Who discovered neutrons in 1932?
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The oil drop experiment helped to determine the charge of a _________.
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Match the following scientists with their contributions:
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What is the purpose of Millikan's oil drop experiment?
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The existence of electrically neutral particles was felt necessary as one of the constituents of an atom.
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The properties of fundamental particles are given in _____________.
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What is the formula for the energy of the stationary states associated with hydrogen-like species?
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The frequency of the photon is given by the equation ν = ∆E / h.
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What is the expression for the radius of the stationary states associated with hydrogen-like species?
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The energy of the stationary states associated with hydrogen-like species is given by the expression E n = − 2.18 ×10 −18 _________________ J.
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Match the following expressions with their corresponding physical quantities:
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What is the unit of energy associated with the absorption and emission of a photon?
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The term in the parenthesis is negative in case of absorption spectrum.
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What is the formula for the wavenumber of the photon?
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The frequency of the photon is given by the equation ________________________ = ∆E / h.
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Study Notes
Bohr's Theory
- Bohr's theory can be applied to ions containing only one electron, such as He+, Li2+, Be3+, etc.
- The energies of the stationary states associated with these ions are given by the expression: E_n = -2.18 × 10^(-18) × (Z^2 / n^2) J
- The radii of these ions are given by the expression: r_n = 52.9 × (n^2 / Z) pm
Energy and Frequency
- The energy change (ΔE) associated with the absorption and emission of a photon can be evaluated using the equation: ΔE = R_H × (1 / n_i^2 - 1 / n_f^2)
- The frequency (ν) associated with the absorption and emission of a photon can be evaluated using the equation: ν = ΔE / h
- The wavenumber (ν) can be evaluated using the equation: ν = R_H × (1 / n_i^2 - 1 / n_f^2) / hc
Absorption and Emission Spectra
- In the case of absorption spectra, n_f > n_i and the term in the parenthesis is positive, indicating that energy is absorbed.
- In the case of emission spectra, n_f < n_i and the term in the parenthesis is negative, indicating that energy is emitted.
Line Spectrum of Hydrogen
- The line spectrum observed in the case of hydrogen can be explained quantitatively using Bohr's model.
- According to Bohr's model, radiation (energy) is absorbed if the electron moves from an orbit of smaller principal quantum number to an orbit of higher principal quantum number.
- The energy gap between the two orbits is given by the equation: ΔE = E_f - E_i
Atomic Models
- The atomic models were proposed to explain the distributions of sub-atomic particles in an atom.
- J.J. Thomson proposed a model of the atom that was later improved upon by Ernest Rutherford.
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Description
Learn about Bohr's theory, its application to ions, and the formulas for energy and radii of stationary states. Understand the energy change associated with absorption and emission of photons.