(i)
The principal quantum number of the initial state of an atom as it emits an
(i)
Answer to Problem 1OQ
Option (e), 5 is the principal quantum number of the initial state of an atom as it emits an
Explanation of Solution
The principal quantum number corresponding to the M shell is 3, and the
Conclusion:
Since the electrons emits from the
Since the electrons fails to emit from the K shell, option (a) is incorrect.
Since the electrons are not coming from the L shell, option (b) is incorrect.
Since the electrons cannot emit from M shell to produce
Since the electrons are not excited from the N shell, option (d) is incorrect.
(ii)
The principal quantum number of the final state of an atom as it emits an
(ii)
Answer to Problem 1OQ
Option (c), 3 is the principal quantum number.
Explanation of Solution
The principal quantum number corresponding to the M shell is 3, and the
Conclusion:
Since final state is M shell whose principal quantum number is
The principal quantum number of the final state is not
The principal quantum number of the final state is not
The principal quantum number of the final state is not
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Chapter 42 Solutions
Bundle: Physics for Scientists and Engineers with Modern Physics, Loose-leaf Version, 9th + WebAssign Printed Access Card, Multi-Term
- (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_forwardCompute 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_forwarda)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_forwardHydrogen 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_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
- What is the energy in eV and wavelength in µm of a photon that, when absorbed by a hydrogen atom, could cause a transition from the n = 4 to the n = 6 energy level? (a) energy in eV? (b) wavelength in µm?arrow_forwardThe hydrogen atom was initially at the state where n=3 and l=2. It then decays to a lower state releasing a photon. What are the possible photon energies(in [eV]) that may be observed?arrow_forwardAngular momentum and Spin. An electron in an H-atom has orbital angular momentum magnitude and z-component given by L² = 1(1+1)ħ², 1 = 0,1,2,..., n-1 Lz = m₂ħ, m₁ = 0, ±1, ±2,..., ±l 3 S² = s(s+1)h² = h², 4 Consider an excited electron (n > 1) on an H-atom. Sz = msh 1 =+=ħ Show that the minimum angle that the I can have with the z-axis is given by n-1 n L.min = cos Clue: the angle a vector with magnitude V from the z-axis can be computed from cos 0 = V²/Varrow_forward
- Principles of Physics: A Calculus-Based TextPhysicsISBN:9781133104261Author:Raymond A. Serway, John W. JewettPublisher:Cengage Learning