EBK PHYSICS FOR SCIENTISTS & ENGINEERS
5th Edition
ISBN: 9780134296074
Author: GIANCOLI
Publisher: VST
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An electron is in the nth Bohr orbit of the hydrogen atom. (a) Show that the period of the electron is T = n3t0 and determine the numerical value of t0. (b) On average, an electron remains in the n = 2 orbit for approximately 10 ms before it jumps down to the n = 1 (ground-state) orbit. How many revolutions does the electron make in the excited state? (c) Define the period of one revolution as an electron year, analogous to an Earth year being the period of the Earth’s motion around the Sun. Explain whether we should think of the electron in the n = 2 orbit as “living for a long time.”
(a) What quantum numbers are needed to give a complete description of the quantum
state of an electron in an atom?
(b) List the value of each of the quantum numbers mentioned in (a) for each of the
electrons in a neutral strontium atom in its ground state.
The electron of a hydrogen atom is in an orbit with radius of 8.46 Å (1 Å = 10-10 m), according to the Bohr model. Which of the following statements is correct?
a) The total energy of the orbit is –13.6 eV, and the kinetic energy is +13.6 eV.
b) The total energy of the orbit is –0.85 eV, and the potential energy is –1.70 eV.
c) The total energy of the orbit is –0.85 eV, and the potential energy is +1.70 eV.
d) The total energy of the orbit is –0.85 eV, and the potential energy is –0.85 eV.
e) The total energy of the orbit is –3.40 eV, and the potential energy is –6.80 eV.
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Similar questions
- The Balmer series for hydrogen was discovered before either the Lyman or the Paschen series. Why?arrow_forward(a) Using Bohr’s second postulate of quantization of orbital angular momentum show that the circumference of the electron in the n,h orbital state in hydrogen atom is n times the de-Broglie wavelength associated with it. (b) 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?arrow_forwardThe gravitational attraction between electron and proton in a hydrogen atom is weaker than the coulomb attraction by a factor of about 10-40. An alternative way of looking at this fact is to estimate the radius of the first Bohr orbit of a hydrogen atom if the electron and proton were bound by gravitational attraction. You will find the answer interesting.arrow_forward
- In accordance with the Bohr’s model, find the quantum number that characterises the earth’s revolution around the sun in an orbit of radius 1.5×1011 m with orbital speed 3 × 104 m/s. (Mass of earth= 6.0 × 1024 kg.)arrow_forward(a) Using the Bohr model, calculate the speed of the electron in a hydrogen atom in the n = 1, 2, and 3 levels. (b) Calculate the orbital period in each of these levels. (c) The average lifetime of the first excited level of a hydrogen atom is 1.0 * 10-8 s. In the Bohr model, how many orbits does an electron in the n = 2 level complete before returning to the ground level?arrow_forward(a) Using de-Broglie’s hypothesis, explain with the help of a suitable diagram, Bohr’s second postulate of quantization of energy levels in a hydrogen atom. (b) The ground state energy of hydrogen atom is -13.6 eV. What are the kinetic and potential energies of the state?arrow_forward
- A hydrogen atom is in its third excited state (n = 4). Using the Bohr theory of the atom, calculate the following. (a) the radius of the orbit nm (b) the linear momentum of the electron kg • m/s (c) the angular momentum of the electron J.S (d) the kinetic energy eV (e) the potential energy eV (f) the total energy eVarrow_forward(a) If an electron makes a transition from the n = 4 Bohr orbit to the n = 2 orbit, determine the wavelength of the photon created in the process. (b) Assuming that the atom was initially at rest, determine the recoil speed of the hydrogen atom when this photon is emitted.arrow_forwardA hydrogen atom is in its second excited state (n = 3). Using the Bohr theory of the atom, calculate the following. (a) the radius of the orbit nm(b) the linear momentum of the electron kg · m/s(c) the angular momentum of the electron J · s(d) the kinetic energy eV(e) the potential energy eV(f) the total energy eVarrow_forward
- (a) Using the Bohr’s model calculate the speed of the electron in a hydrogen atom in the n = 1, 2, and 3 levels. (b) Calculate the orbital period in each of these levels.arrow_forwardIn accordance with the Bohr's model, find the quantum number that characterises the earth's revolution around the sun in an orbit of radius 1.5 x 10" m with orbital speed 3 x 104 m/s. (Mass of earth = 6.0 x 1024 kg.)arrow_forwardWrite an expression relating the kinetic energy KE of the electron and the potential energy PE in the Bohr model of the hydrogen atom. (a) Suppose a hydrogen atom absorbs a photon of energy E, resulting in the transfer of the electron to a higher - energy level. Express the resulting change in the potential energy of the system in terms of E. (b) What is the change in the electron’s kinetic energy during this process?arrow_forward
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