Principles of Physics: A Calculus-Based Text
5th Edition
ISBN: 9781133104261
Author: Raymond A. Serway, John W. Jewett
Publisher: Cengage Learning
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Question
Chapter 29, Problem 10OQ
(i)
To determine
The correct principle quantum number for initial state of an atom as it emits an
(ii)
To determine
The correct principle quantum number for the final state of an atom as it emits an
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a) Calculate the energy of the emissive transition with the lowest energy possible for the Lyman series, for a mole of hydrogen atoms. Express your answer in joules/mol.
b) Is this transition in the visible spectral domain? If not, in which region is it located?
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Chapter 29 Solutions
Principles of Physics: A Calculus-Based Text
Ch. 29.2 - Prob. 29.1QQCh. 29.2 - Prob. 29.2QQCh. 29.4 - Prob. 29.3QQCh. 29.5 - Prob. 29.4QQCh. 29.6 - Prob. 29.5QQCh. 29.6 - Prob. 29.6QQCh. 29 - Prob. 1OQCh. 29 - Prob. 2OQCh. 29 - Prob. 3OQCh. 29 - Prob. 4OQ
Ch. 29 - Prob. 5OQCh. 29 - Prob. 6OQCh. 29 - Prob. 7OQCh. 29 - Prob. 8OQCh. 29 - Prob. 9OQCh. 29 - Prob. 10OQCh. 29 - Prob. 1CQCh. 29 - Prob. 2CQCh. 29 - Prob. 3CQCh. 29 - Prob. 4CQCh. 29 - Prob. 5CQCh. 29 - Prob. 6CQCh. 29 - Prob. 7CQCh. 29 - Prob. 8CQCh. 29 - Prob. 9CQCh. 29 - Prob. 10CQCh. 29 - Prob. 1PCh. 29 - Prob. 2PCh. 29 - Prob. 3PCh. 29 - Prob. 4PCh. 29 - Prob. 5PCh. 29 - Prob. 6PCh. 29 - Prob. 7PCh. 29 - Prob. 8PCh. 29 - Prob. 10PCh. 29 - Prob. 11PCh. 29 - Prob. 12PCh. 29 - Prob. 13PCh. 29 - Prob. 14PCh. 29 - Prob. 15PCh. 29 - Prob. 16PCh. 29 - Prob. 17PCh. 29 - Prob. 18PCh. 29 - Prob. 19PCh. 29 - Prob. 20PCh. 29 - Prob. 21PCh. 29 - Prob. 22PCh. 29 - Prob. 23PCh. 29 - Prob. 24PCh. 29 - Prob. 25PCh. 29 - Prob. 26PCh. 29 - Prob. 27PCh. 29 - Prob. 28PCh. 29 - Prob. 29PCh. 29 - Prob. 30PCh. 29 - Prob. 31PCh. 29 - Prob. 32PCh. 29 - Prob. 33PCh. 29 - Prob. 34PCh. 29 - Prob. 35PCh. 29 - Prob. 36PCh. 29 - Prob. 37PCh. 29 - Prob. 38PCh. 29 - Prob. 39PCh. 29 - Prob. 40PCh. 29 - Prob. 41PCh. 29 - Prob. 42PCh. 29 - Prob. 43PCh. 29 - Prob. 44PCh. 29 - Prob. 45PCh. 29 - Prob. 46PCh. 29 - Prob. 47PCh. 29 - Prob. 48PCh. 29 - Prob. 49PCh. 29 - Prob. 50PCh. 29 - Prob. 51PCh. 29 - Prob. 52PCh. 29 - Prob. 53PCh. 29 - Prob. 54PCh. 29 - Prob. 55PCh. 29 - Prob. 57PCh. 29 - Prob. 58PCh. 29 - Prob. 59PCh. 29 - Prob. 60PCh. 29 - Prob. 61PCh. 29 - Prob. 63PCh. 29 - Prob. 64PCh. 29 - Prob. 65PCh. 29 - Prob. 66P
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- I:26)arrow_forwardv) A hydrogen atom makes a transition from a bound state (Energy of the bound state = 0.32 eV) to a state with excitation energy (= 10.2 eV). Calculate the energy of the photon emitted.arrow_forward(a) The Lyman series in hydrogen is the transition from energy levels n = 2, 3, 4, ... to the ground state n = 1. The energy levels are given by 13.60 eV En n- (i) What is the second longest wavelength in nm of the Lyman series? (ii) What is the series limit of the Lyman series? [1 eV = 1.602 x 1019 J, h = 6.626 × 10-34 J.s, c = 3 × 10° m.s] %3D Two emission lines have wavelengts A and + A2, respectively, where AA <<2. Show that the angular separation A0 in a grating spectrometer is given aproximately by (b) A0 = V(d/m)-2 where d is the grating constant and m is the order at which the lines are observed.arrow_forward
- Compute the intrinsic line-width (Δλ) of the Lyman α line (corresponding to the n=2 to n=1) transition for the Hydrogen atom. You may assume that the electron remains in the excited state for a time of the order of 10^−8s. The line-width may be computed using:ΔE=(hc/λ^2)Δλarrow_forward(d) The following orbital belongs to the 3d subshell of the Hydrogen atom: r Y(r, 0, 0) = A(Z) θ, φ) 2 r e 3ao sin² (0) e²i зао where A and ao are constants. Using the operator for the z-component of orbital angular momentum (L₂ = -ih d/do) determine the m, for this particular orbital. (e) Consider the wavefunction, r r Y(r,0,0) = A-e 2do cos(0) do (i) Identify the radial part of this orbital function and the number of radial nodes. (ii) Identify the angular part of the orbital function and the number of angular nodes. Z (iii) Using this information and the L₂ = -ih d/do operator obtain the n, 1, and, m quantum numbers and identify the orbital.arrow_forward(a) A simplified parabolic E-K diagram for an electron in the conduction band is given in Figure 3. Determine the relative effective mass, m'/m.. given the E – E. = C,k², value of a of 1 nm, Planck constant h = 6.625 × 10-34 J. s, free electron mass m, = 9.11 x 10-31 kg, electric charge q = 1.6 x 10-19 C and 1 eV = 1.6 x 10-19 J. E E = E,+0.32 eV Figure 3arrow_forward
- a)Suppose a hydrogen molecule in its ground state is dissociated by absorbing a photon of ultraviolet light, causing the two hydrogen atoms to fly apart. What photon energy will give each atom a speed of 19 km/s? The mass of a hydrogen atom is 1.7×10^−27 kg Express your answer to two significant figures and include the appropriate units.arrow_forwardQ) A hydrogen atom emits radiation as a result of an electron transition to a lower energy level. Determine the highest frequency possible due to this transition if the atom emits a series of lines that lie in the visible part of the spectrum. Then, if the electron ends up in n = 1 level, prove that the atom emits a series of lines of wavelength that are not in the visible part of the spectrum.arrow_forward(b) A photon is emitted by a doubly ionised lithium atom (Li²+) when an electron makes a transition to the ground state. The wavelength of the photon is measured to be 10.83 nanometres. Determine the principal quantum number and the energy of the initial state The atomic number of lithium is Z = 3.arrow_forward
- Hydrogen atoms can emit four spectral lines with visible colors between red and violet. (a) What is the longest, second longest, third longest, and shortest wavelength in the visible range? (b) What are the two quantum numbers of two states involved in the transition? (For the longest, second longest, third longest, and shortest wavelength)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_forwardRecall that for practical purposes the number of orbits in the Bohr model of the hydrogen atom is limited to 7, however the model can in theory be extend to n = ∞. This idea of orbits beyond 7 is employed in the following question. Also it may be useful to know that 1 ∞2 = 0. The ionization energy associated with an atom equals the amount of energy required to strip a given electron away from its nucleus in the gaseous phase. For purposes of this question/calculation, if we consider the electron of a hydrogen atom in orbit n = 12 to be sufficiently removed from the nucleus, so as to be free of its electrostatic hold (i.e. to be stripped of its nucleus), what is the ionization energy for hydrogen in kJ/mol? Express your answer correctly rounded to 2 decimal places.arrow_forward
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