Definitions [5]
- The collection of different spectral lines obtained due to transition of an electron in hydrogen atom from upper energy levels to lower energy levels is called the Hydrogen Spectrum.
- The hydrogen spectrum consists of specific wavelengths of light emitted by hydrogen atoms. When transition of an electron in a hydrogen atom occurs between energy levels, it emits or absorbs photons of certain wavelengths, creating a series of lines known as the hydrogen spectrum.
The spectrum consisting of bright lines on a dark background, emitted when an atomic gas is excited at low pressure by passing an electric current through it, is called the Emission Line Spectrum.
Dark spectral absorption lines are the lines seen in a continuous spectrum at the frequencies absorbed by the atoms of a rarefied gas.
When an atom absorbs a photon having precisely the same energy as that required for an electron in a lower energy state to make a transition to a higher energy state, the process is called absorption.
OR
Absorption is the process in which an atom takes in a photon whose energy exactly matches the energy needed for an electronic transition from a lower level to a higher level.
The various lines in atomic spectra are produced when electrons jump from a higher energy state to a lower energy state, and photons are emitted. These spectral lines are called emission lines.
OR
Emission lines are the spectral lines produced when electrons fall from higher energy states to lower energy states and emit photons.
Formulae [5]
If the distance between the alpha-particle and the nucleus is rr, then the electrostatic force between them is given by:
F = \[\frac {1}{4πε_0}\] ⋅ \[\frac{2e\cdot Ze}{r^2}\]
\[L=mvr=\frac{nh}{2\pi},\quad n=1,2,3\ldots\]
\[h\nu=E_2-E_1=\frac{hc}{\lambda}\]
\[\Delta E=h\nu=E_i-E_f\]
\[\frac{1}{\lambda_{\mathrm{vac}}}=R_H\left[\frac{1}{n_1^2}-\frac{1}{n_2^2}\right]\]
where \[R_{H}=1.097\times10^{7}\mathrm{m}^{-1}\] (Rydberg constant)
Theorems and Laws [1]
Bohr's First Postulate:
An atom consists of a small, massive central core called the nucleus, around which planetary electrons revolve. The centripetal force required for their rotation is provided by the electrostatic attraction between the electrons and the nucleus.
Bohr's Second Postulate (Quantum Condition):
The electrons are permitted to circulate only in those orbits in which the angular momentum of an electron is an integral multiple of \[\frac{h}{2\pi}\]; h being Planck's constant.
Bohr's Third Postulate:
While revolving in the permissible orbits, an electron does not radiate energy. These non-radiating orbits are called stationary orbits.
Bohr's Fourth Postulate:
An atom can emit or absorb radiation in the form of discrete energy photons only when an electron jumps from a higher to a lower orbit or from a lower to a higher orbit, respectively.
Key Points
- Rutherford's model could not explain the stability of an atom despite the revolving electrons around the nucleus.
- Electrons revolving around the nucleus emit radiation and subsequently lose energy.
- Loss of energy causes electrons to spiral inward and eventually fall into the nucleus, leading to the collapse of the atom - but this is untrue.
- If continuous energy loss occurred, electrons would fall into the nucleus, making the atom unstable - which contradicts actual observations.
- If electrons emit continuous energy, they should form a continuous spectrum, but actually, a line spectrum is obtained, which Rutherford's model fails to explain.
- Bohr modified Rutherford's model - electrons move in fixed orbital shells, each with fixed energy levels.
- The centripetal force for electron revolution is provided by electrostatic attraction between the electron and the nucleus.
- An electron does not radiate energy while revolving in a stationary orbit.
- Energy is emitted or absorbed only during electron transitions between orbits.
- Limitations of Bohr's Model:
- Fails to explain the Zeeman Effect (effect of high magnetic fields on atomic spectra).
- Contradicts the Heisenberg Uncertainty Principle.
- Unable to explain the spectra of larger/multi-electron atoms.
- Ground state energy of hydrogen = -13.6 eV.
- Ionisation energy of hydrogen in the ground state = 13.6 eV.
- Energy required for first excitation = 10.2 eV.
- Energy required for second excitation = 12.09 eV.
- The energy of a free electron is 0 eV.
- Bohr accepted Rutherford’s nuclear model but modified it using quantum ideas.
- Classical mechanics and electromagnetism could not explain atomic-scale behaviour fully.
- Only certain orbits are allowed for the electron in the hydrogen atom.
- These orbits have definite total energy.
- Electron transitions between energy levels lead to photon emission.
- The energy of the hydrogen atom is negative because the electron is bound to the nucleus.
- Lyman series — transitions to n = 1; region: ultraviolet
- Balmer series — transitions to n = 2; region: visible
- Paschen series — transitions to n = 3; region: infrared
- Brackett series — transitions to n = 4; region: infrared
- Pfund series — transitions to n = 5; region: infrared
- The spectrum of hydrogen is important as most of the universe is made of hydrogen.
- Balmer series involves transitions starting/ending with the first excited state (n = 2) of hydrogen.
- An atom emits radiation when it moves from a higher energy state to a lower energy state.
- The energy difference appears as a photon.
- Because the quantum numbers are integers, only discrete frequencies are emitted.
- These give rise to emission lines.
- If atoms absorb photons of the exact required energy, dark absorption lines appear in a continuous spectrum.
