Definitions [5]
When an atomic gas or vapour at low pressure is excited, it emits radiation of certain wavelengths. The emitted radiation, when analysed with a spectroscope, shows a series of bright lines on a dark background. This type of spectrum is called an emission line spectrum.
When white light from a source passes through an atomic gas or vapour, the gas absorbs radiation of certain wavelengths. As a result, dark lines appear in the otherwise continuous spectrum. This type of spectrum is called an absorption 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 [1]
If the distance between the alpha-particle and the nucleus is rr, then the electrostatic force between them is given by:
F = \[\frac {1}{4πε_0}\] ⋅ \[\frac{2e\cdot Ze}{r^2}\]
Key Points
- 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.
- 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.
- 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.
Important Questions [68]
- In a Geiger-marsden Experiment, Calculate the Distance of Closest Approach to the Nucleus of Z = 80, When a α-particle of 8mev Energy Impinges on It before It Comes Momentarily to Rest and
- Determine the distance of the closest approach when an alpha particle of kinetic energy 3.95 MeV approaches a nucleus of Z = 79, stops and reverses its directions.
- The electron in a hydrogen atom is typically found at a distance of about 5.3 × 10−11 m from the nucleus which has a diameter of about 1.0 × 10−15 m.
- In a Geiger-marsden Experiment, Calculate the Distance of Closest Approach to the Nucleus of Z = 75, When a α-particle of 5 Mev Energy Impinges on It before It Comes Momentarily to Rest and Reverses
- How is the size of a nucleus found experimentally? Write the relation between the radius and mass number of a nucleus.
- An Electron in an Atom Revolves Round the Nucleus in an Orbit of Radius R with Frequency V. Write the Expression for the Magnetic Moment of the Electron.
- The energy of hydrogen atom in an orbit is −1.51 eV. What are kinetic and potential energies of the electron in this orbit?
- A narrow beam of protons, each having 4.1 MeV energy is approaching a sheet of lead (Z = 82). Calculate: the speed of a proton in the beam, and the distance of its closest approach
- Using Rutherford'S Model of the Atom, Derive the Expression for the Total Energy of the Electron in Hydrogen Atom. What is the Significance of Total Negative Energy Possessed by the Electron?
- Differentiate between the 'distance of the closest approach' and the 'impact parameter.'
- Suppose you are given a chance to repeat the alpha-particle scattering experiment using a thin sheet of solid hydrogen in place of the gold foil. (Hydrogen is a solid at temperatures below 14 K.)
- Draw a graph showing the variation of the number of particles scattered (N) with the scattering angle θ in the Geiger-Marsden experiment.
- Answer the Following Question. Explain Briefly How Rutherford Scattering of α-particle by a Target Nucleus Can Provide Information on the Size of the Nucleus.
- A Charged Particle Q is Moving in the Presence of a Magnetic Field B Which is Inclined to an Angle 30° with the Direction of the Motion of the Particle.
- Define the distance of closest approach. An α-particle of kinetic energy 'K' is bombarded on a thin gold foil. The distance of the closest approach is 'r'. What will be the distance of closest approach for an α-particle of double the kinetic energy?
- Write two important limitations of Rutherford's nuclear model of the atom.
- An electron jumps from fourth to first orbit in an atom. How many maximum number of spectral lines can be emitted by the atom? To which series these lines correspond?
- In Both β− and β+ Decay Processes, the Mass Number of a Nucleus Remains the Same, Whereas the Atomic Number Z Increases by One in β− Decay and Decreases by One in β+ Decay. Explain Giving Reason.
- The wavelength of the second line of the Balmer series in the hydrogen spectrum is 4861 Å. Calculate the wavelength of the first line of the same series.
- State Bohr’S Postulate of Hydrogen Atom Which Successfully Explains the Emission Lines in the Spectrum of Hydrogen Atom
- Using Bohr'S Postulates of the Atomic Model, Derive the Expression for Radius of Nth Electron Orbit
- State Bohr'S Postulate to Define Stable Orbits in Hydrogen Atom. How Does De Broglie'S Hypothesis Explain the Stability of These Orbits?
- Using Bohr'S Postulates, Derive the Expression for the Orbital Period of the Electron Moving in the Nth Orbit of Hydrogen Atom ?
- State Bohr Postulate of Hydrogen Atom that Gives the Relationship for the Frequency of Emitted Photon in a Transition.
- Using Bohr’S Postulates, Obtain the Expression for the Total Energy of the Electron in the Stationary States of the Hydrogen Atom.
- Using Bohr’S Postulates, Obtain the Expression for Total Energy of the Electron in the Nth Orbit of Hydrogen Atom.
- Using Bohr’S Postulates, Derive the Expression for the Frequency of Radiation Emitted When Electron in Hydrogen Atom Undergoes Transition from Higher Energy State (Quantum Number Ni) to the Lower
- The Electron in Hydrogen Atom is Initially in the Third Excited State. What is the Maximum Number of Spectral Lines Which Can Be Emitted When It Finally Moves to the Ground State?
- Using Bohr’S Postulates for Hydrogen Atom, Show that the Total Energy (E) of the Electron in the Stationary States Tan Be Expressed as the Sum of Kinetic Energy (K) and Potential Energy
- Write the Expression for Bohr’S Radius in Hydrogen Atom ?
- Obtain Bohr’S Quantisation Condition for Angular Momentum of Electron Orbiting in Nth Orbit in Hydrogen Atom on the Basis of the Wave Picture of an Electron Using De Broglie Hypothesis.
- Answer the Following Question. Calculate the Orbital Period of the Electron in the First Excited State of the Hydrogen Atom.
- When the electron orbiting in hydrogen atom in its ground state moves to the third excited state, show how the de Broglie wavelength associated with it would be affected.
- Use Bohr’s model of hydrogen atom to obtain the relationship between the angular momentum and the magnetic moment of the revolving electron.
- Calculate the de-Broglie wavelength associated with the electron revolving in the first excited state of the hydrogen atom. The ground state energy of the hydrogen atom is −13.6 eV.
- Use Bohr's postulate to prove that the radius of nth orbit in a hydrogen atom is proportional to n2.
- How will the energy of a hydrogen atom change if n increases from 1 to ∞?
- State Bohr's postulate to explain stable orbits in a hydrogen atom. Prove that the speed with which the electron revolves in nth orbit is proportional to n(1n).
- What is meant by ionisation energy?
- Write the ionisation energy value for the hydrogen atom.
- Specify the transition of an electron in the wavelength of the line in the Bohr model of the hydrogen atom which gives rise to the spectral line of the highest wavelength ______.
- The radius of the nth orbit in the Bohr model of hydrogen is proportional to ______.
- State three postulates of Bohr's theory of hydrogen atom.
- Find the angular momentum of an electron revolving in the second orbit in Bohr's hydrogen atom.
- State Bohr'S Quantization Condition for Defining Stationary Orbits.
- Using Bohr'S Postulates, Derive the Expression for the Total Energy of the Electron in the Stationary States of the Hydrogen Atom ?
- Using Bohr’S Postulates, Obtain the Expressions for (I) Kinetic Energy and (Ii) Potential Energy of the Electron in Stationary State of Hydrogen Atom.
- The Energy Levels of an Atom Are as Shown Below. Which of Them Will Result in the Transition of a Photon of Wavelength 275 Nm?
- A Hydrogen Atom Initially in the Ground Level Absorbs a Photon, Which Excites It to the N = 4 Level. Determine the Wavelength and Frequency of the Photon.
- Given the Ground State Energy E0 = - 13.6 eV and Bohr Radius a0 = 0.53 A. Find Out How the De Broglie Wavelength Associated with the Electron Orbiting in the Ground State Would Change When It Jumps into the First Excited State.
- A 12.3 Ev Electron Beam is Used to Bombard Gaseous Hydrogen at Room Temperature. Upto Which Energy Level the Hydrogen Atoms Would Be Excited?
- A 12.9 Ev Beam of Electronic is Used to Bombard Gaseous Hydrogen at Room Temperature. Upto Which Energy Level the Hydrogen Atoms Would Be Excited ?
- The diagram shows the four energy levels of an electron in the Bohr model of the hydrogen atom. Identify the transition in which the emitted photon will have the highest energy.
- Draw the Energy Level Diagram Showing How the Line Spectra Corresponding to Paschen Series Occur Due to Transition Between Energy Levels.
- The ground state energy of a hydrogen atom is −13.6 eV. What are the kinetic and potential energies of the electron in this state?
- A 12.5 eV Electron Beam is Used to Bombard Gaseous Hydrogen at Room Temperature. Upto Which Energy Level the Hydrogen Atoms Would Be Excited? Calculate the Wavelengths of the First Member of Lyman and First Member of Balmer Series.
- Which Transition Corresponds to Emission of Radiation of Maximum Wavelength?
- A 12.5 eV electron beam is used to bombard gaseous hydrogen at room temperature. What series of wavelengths will be emitted?
- A hydrogen atom makes a transition from n = 5 to n = 1 orbit. The wavelength of photon emitted is λ. The wavelength of photon emitted when it makes a transition from n = 5 to n = 2 orbit is ______.
- Find the Wavelength of the Electron Orbiting in the First Excited State in Hydrogen Atom.
- Calculate the Shortest Wavelength of the Spectral Lines Emitted in Balmer Series.
- How Would the Ionization Energy Change When Electron in Hydrogen Atom is Replaced by a Particle of Mass 200 Times that of Electron but Having the Same Charge ?
- Define Ionization Energy.
- Using Bohr’S Second Postulate of Quantization of Orbital Angular Momentum Show that the Circumference of the Electron in the Nth Orbital State in Hydrogen Atom is N Times the De Broglie Wavelength
- Answer the Following Question. State Bohr'S Quantization Condition of Angular Momentum. Calculate the Shortest Wavelength of the Bracket Series and State to Which Part of the Electromagnetic
- Show that the Radius of the Orbit in Hydrogen Atom Varies an N X N,Where N is the Principal Quantum Number of the Atom.
- Plot a Graph Showing the Variation of De Broglie Wavelength (X) Associated with a Charged a Particle of Mass M, Versus 1 √ V Where V
- How Does One Explain, Using De Broglie Hypothesis, Bohr'S Second Postulate of Quantization of Orbital Angular Momentum?
