Questions based on the Bohr model of hydrogen atom are inevitable in any Medical and Engineering test paper. Consider the following two questions which appeared in A.I.I.M.S.- 2005 test paper:
(1) Solid targets of different elements are bombarded by highly energetic electron beams. The frequency (f) of the characteristic X-rays emitted from different targets varies with atomic number Z as
(a) f α √Z (b) f α Z2 (c) f α Z (d) f α Z3/2
As you might have noted, X-rays are produced by electron transitions from outer orbits to inner orbits. But atoms of high atomic number are required for the production of X-rays since the X-ray photon has much greater energy compared to light photon. The energy of the electron in an orbit is directly proportional to Z2. [Note that in a hydrogen like atom, the energy is -13.6 Z2/n2 electron volt]. The energy difference between levels also is directly proportional to Z2. Since the energy difference is equal to hν where ‘ν’ is the frequency of the radiation emitted, the correct option is (b).
[More rigorous treatment shows that ν α (Z-b)2 where b is a constant for a given spectral series].
(2) The ground state energy of hydrogen atom is -13.6 eV. What is the potential energy of the atom in this state?
(a) 0 eV (b) -27.2 eV (c) 1eV (d) 2 eV
The correct option is (b) since the potential energy is twice the kinetic energy. You should note that in all cases of central field motion under inverse square law attractive force, the total energy and potential energy are negative and the potential energy is twice the total energy.
Suppose we modify this question as follows:
The ground state energy of hydrogen atom is -13.6 eV. What is the kinetic energy of the electron in this state?
(a) -13.6 eV (b) -27.2 eV (c) 0 eV (d) 13.6 eV
(1) Solid targets of different elements are bombarded by highly energetic electron beams. The frequency (f) of the characteristic X-rays emitted from different targets varies with atomic number Z as
(a) f α √Z (b) f α Z2 (c) f α Z (d) f α Z3/2
As you might have noted, X-rays are produced by electron transitions from outer orbits to inner orbits. But atoms of high atomic number are required for the production of X-rays since the X-ray photon has much greater energy compared to light photon. The energy of the electron in an orbit is directly proportional to Z2. [Note that in a hydrogen like atom, the energy is -13.6 Z2/n2 electron volt]. The energy difference between levels also is directly proportional to Z2. Since the energy difference is equal to hν where ‘ν’ is the frequency of the radiation emitted, the correct option is (b).
[More rigorous treatment shows that ν α (Z-b)2 where b is a constant for a given spectral series].
(2) The ground state energy of hydrogen atom is -13.6 eV. What is the potential energy of the atom in this state?
(a) 0 eV (b) -27.2 eV (c) 1eV (d) 2 eV
The correct option is (b) since the potential energy is twice the kinetic energy. You should note that in all cases of central field motion under inverse square law attractive force, the total energy and potential energy are negative and the potential energy is twice the total energy.
Suppose we modify this question as follows:
The ground state energy of hydrogen atom is -13.6 eV. What is the kinetic energy of the electron in this state?
(a) -13.6 eV (b) -27.2 eV (c) 0 eV (d) 13.6 eV
The correct option is (d) since the kinetic energy is always positive and its magnitude is the same as that of the total energy. This is true in all cases of central field motion under an attractive inverse square law force, as in the case of the motion of a satellite around a planet.
You will find more multiple choice questions (with solution) at physicsplus: Questions on Bohr Atom Model
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