Q. 154.7( 11 Votes )
The total energy of an electron in the first excited state of the hydrogen atom is about –3.4 eV.
(a) What is the kinetic energy of the electron in this state?
(b) What is the potential energy of the electron in this state?
(c) Which of the answers above would change if the choice of the zero of potential energy is changed?
(a) Given: The total energy of an electron in the first excited state of the hydrogen atom is about –3.4 eV.
Kinetic energy of the electron in this state = negative of the total energy = -E
Kinetic energy of the electron in this state =-(-3.4)eV = + 3.4 eV
(b) Potential energy is given as the negative of the twice of the kinetic energy
U = -2 (3.4) eV
U = -6.8eV
(c) If the choice of the zero of potential energy is changed, then the value of potential energy of the system also changes and as we know the total energy is sum of kinetic energy as well as potential energy. Therefore, the potential energy will also changes.
Rate this question :
(a) State Bohr’s postulate to define stable orbits in hydrogen atom. How does de Broglie’s hypothesis explain the stability of these orbits ?
(b) A hydrogen atom initially in the ground state absorbs a photon which excites it to the n = 4 level. Estimate the frequency of the photon.Physics - Board Papers
The Bohr model for the H-atom relies on the Coulomb’s law of electrostatics. Coulomb’s law has not directly been verified for very short distances of the order of angstroms. Supposing Coulomb’s law between two opposite charge +q1, –q2 is modified to
Calculate in such a case, the ground state energy of a H-atom, if ε = 0.1, R0 = 1Å.
Physics - Exemplar
Consider an excited hydrogen atom in state n moving with a velocity v (v << c). It emits a photon in the direction of its motion and changes its state to a lower state m. Apply momentum and energy conservation principles to calculate the frequency v of the emitted radiation. Compare this with the frequency v0 emitted if the atom were at rest.HC Verma - Concepts of Physics Part 2
Suppose in an imaginary world the angular momentum is quantized to be even integral multiples of h/2π. What is the longest possible wavelength emitted by hydrogen atoms in visible range in such a world according to Bohr’s model?HC Verma - Concepts of Physics Part 2
In the Auger process an atom makes a transition to a lower state without emitting a photon. The excess energy is transferred to an outer electron which may be ejected by the atom. (This is called an Auger electron). Assuming the nucleus to be massive, calculate the kinetic energy of an n = 4 Auger electron emitted by Chromium by absorbing the energy from a n = 2 to n = 1 transition.Physics - Exemplar
A uniform magnetic field B exists in a region. An electron projected perpendicular to the field goes in a circle. Assuming Bohr’s quantization rule for angular momentum, calculate
(a) the smallest possible radius of the electron
(b) the radius of the nth orbit and
(c) the minimum possible speed of the electron.
HC Verma - Concepts of Physics Part 2
Consider a neutron and an electron bound to each other due to gravitational force. Assuming Bohr’s quantization rule for angular momentum to be valid in this case, derive an expression for the energy of the neutron-electron system.HC Verma - Concepts of Physics Part 2
Deuterium was discovered in 1932 by Harold Urey by measuring the small change in wavelength for a particular transition in 1H and 2H. This is because, the wavelength of transition depend to a certain extent on the nuclear mass. If nuclear motion is taken into account then the electrons and nucleus revolve around their common center of mass. Such a system is equivalent to a single particle with a reduced mass μ, revolving around the nucleus at a distance equal to the electron-nucleus separation. Here μ = meM/ (me + M) where M is the nuclear mass and me is the electronic mass. Estimate the percentage difference in wavelength for the 1st line of the Lyman series in 1H and 2H. (Mass of 1H nucleus is 1.6725 × 10–27 kg, Mass of 2H nucleus is 3.3374 × 10–27 kg, Mass of electron = 9.109 × 10-31 kg.)Physics - Exemplar
Light from Balmer series of hydrogen is able to eject photoelectrons from a metal. What can be the maximum work function of the metal?HC Verma - Concepts of Physics Part 2
A neutron having kinetic energy 12.5 eV collides with a hydrogen atom at rest. Neglect the difference in mass between the neutron and the hydrogen atom and assume that the neutron does not leave its line of motion. Find the possible kinetic energies of the neutron after the even.HC Verma - Concepts of Physics Part 2