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The binding energy of a valence electron in a Li atom in the states 2S and 2P is equal to 5.39 and 3.54 eV respectively. Find the Rydberg corrections for S and P terms of the atom.
Find the Rydberg correction for the 3P term of a Na atom whose first excitation potential is 2.10 V and whose valence electron in the normal 3S state has the binding energy 5.14 eV.
Find the binding energy of a valence electron in the ground state of a Li atom if the wavelength of the first line of the sharp series is known to be equal to λ1 = 813 nm and the short-wave cut-off wavelength of that series to λ2 = 350 nm.
Determine the wavelengths of spectral lines appearing on transition of excited Li atoms from the state 3S down to the ground state 2S. The Rydberg corrections for the S and P terms are – 0.41 and – 0.04.
The wavelengths of the yellow doublet components of the resonance Na line caused by the transition 3P → 3S are equal to 589.00 and 589.56 nm. Find the splitting of the 3P term in eV units.
The first line of the sharp series of atomic cesium is a doublet with wavelengths 1358.8 and 1469.5 nm. Find the frequency intervals (in rad/s units) between the components of the sequent lines of that series.
Write the spectral designations of the terms of the hydrogen atom whose electron is in the state with principal quantum number n = 3.
How many and which values, of the quantum number J can an atom possess in the state with quantum numbers S and L equal respectively to
(a) 2 and 3;
(b) 3 and 3;
(c) 5/2 and 2?
Find the possible values of total angular moment a of atoms in the states 4P and 5D.
Find the greatest possible total angular momentum and the corresponding spectral designation of the term
(a) Of a Na atom whose valence electron possesses the principal quantum number n = 4;
(b) Of an atom with electronic configuration 1s22p3d.
It is known that in F and D states the number of possible values of the quantum number J is the same and equal to five. Find the spin angular momentum in these states.
An atom is in the state whose multiplicity is three and the total angular momentum is h √2-0. What can the corresponding quantum number L be equal to?
Find the possible multiplicities × of the terms of the types
(a) ×D2;
(b) ×P3/2;
(c) ×F1.
A certain atom has three electrons (s, p, and d), in addition to filled shells, and is in a state with the greatest possible total mechanical moment for a given configuration. In the corresponding vector model of the atom find the angle between the spin momentum and the total angular momentum of the given atom.
An atom possessing the total angular momentum h√6 is in the state with spin quantum number S = t. In the corresponding vector model the angle between the spin momentum and the total angular momentum is θ = 73.2°. Write the spectral symbol for the term of that state.
Write the spectral symbols for the terms of a two-electron system consisting of one p electron and one d electron.
A system comprises an atom in 2P3/2 state and a d electron. Find the possible spectral terms of that system.
Find out which of the following transitions are forbidden by the selection rules: 2D3/2, → 2P½, 3P1 → 2S1/2, 3F3, → 3P2, 4F7/2 → 4D5/2.
Determine the overall degeneracy of a 3D state of a Li atom. What is the physical meaning of that value?
Find the degeneracy of the states 2P, 3D, and 4F possessing the greatest possible values of the total angular momentum.
Write the spectral designation of the term whose degeneracy is equal to seven and the quantum numbers L and S are interrelated as L = 3S.
What element has the atom whose K, L, and M shells and 4s sub shell are filled completely and 4p sub shell is half-filled?
Using the Hund rules, find the basic term of the atom whose partially filled sub shell contains
(a) Three p electrons;
(b) Four p electrons.
Using the Hund rules, find the total, angular momentum of the atom in the ground state whose partially filled sub shell contains
(a) Three d electrons;
(b) Seven d electrons
Making use of the Hund rules, find the number of electrons in the only partially filled sub shell of the atom whose basic term is
(a) 3Ft2;
(b) 2P3/2;
(c) 6S5/2.
Using the Hund rules, write the spectral symbol of the basic term of the atom whose only partially filled sub shell
(a) Is filled by 1/3, and S = t;
(b) Is filled by 70%, and S = 3/2.
The only partially filled sub shell of a certain atom contains three electrons, the basic term of the atom having L = 3. Using the Hund rules, write the spectral symbol of the ground state of the given atom.
Using the Hund rules, find the magnetic moment of the ground state of the atom whose open sub shell is half-filled with five electrons.
What fraction of hydrogen atoms is in the state with the principal quantum number n = 2 at a temperature T = 3000 K?
Find the ratio of the number of atoms of gaseous sodium in the state 3S to that in the ground state 3S at a temperature T = 2400 K. The spectral line corresponding to the transition 3P → 3S is known to have the wavelength λ = 589 nm.
Calculate the mean lifetime of excited atoms if it is known that the intensity of the spectral line appearing due to transition to the ground state diminishes by a factor η = 25 over a distance l = 2.5 mm along the stream of atoms whose velocity is v = 600 m/s.
Rarefied Hg gas whose atoms are practically all in the ground state was lighted by a mercury lamp emitting a resonance line of wavelength λ = 253.65 rim. As a result, the radiation power of Hg gas at that wavelength turned out to be P = 35 mW. Find the number of atoms in the state of resonance excitation whose mean lifetime is z = 0.15μs.
Atomic lithium of concentration n = 3.6.1016 cm –3 is at a temperature T = 1500 K. In this case the power emitted at the resonant line's wavelength λ = 671 nm (2P → 2S) per unit volume of gas is equal to P = 0.30 W/cm a. Find the mean lifetime of Li atoms in the resonance excitation state.
Atomic hydrogen is in thermodynamic equilibrium with its radiation. Find:
(a) The ratio of probabilities of induced and spontaneous radiations of the atoms from the level 2P at a temperature T = 3000 K;
(b) The temperature at which these probabilities become equal.
A beam of light of frequency w, equal to the resonant frequency of transition of atoms of gas, passes through that gas heated to temperature T. In this case hw >> kT. Taking into account induced radiation, demonstrate that the absorption coefficient of the gas × varies as × = ×o (1 – e–hw/kt), where ×o is the absorption coefficient for T → 0.
The wavelength of a resonant mercury line is λ = 253.65 nm. The mean lifetime of mercury atoms in the state of resonance excitation is z = 0.15μs. Evaluate the ratio of the Doppler line broadening to the natural line width at a gas temperature T =300K.
Find the wavelength of the Kα line in copper (Z = 29) if the wavelength of the Kα line in iron (Z = 26) is known to be equal to 193 pm.
Proceeding from Moseley's law find:
(a) The wavelength of the Kα line in aluminium and cobalt:
(b) The difference in binding energies of K and L electrons in vanadium.
How many elements are there in a row between those whose wavelengths of Kα lines are equal to 250 and i79 pro?
Find the voltage applied to an X-ray tube with nickel anticathode if the wavelength difference between the Ks line and the short-wave cut-off of the continuous X-ray spectrum is equal to 84 pro.
At a certain voltage applied to an X-ray tube with aluminium anticathode the short-wave cut-off wavelength of the continuous X-ray spectrum is equal to 0.50 nm. Will the K series of the characteristic spectrum whose excitation potential is equal to 1.56 kV be also observed in this case?
When the voltage applied to an X-ray tube increased from V1 = 10 kV to V2 = 20 kV, the wavelength interval between the Ks line and the short-wave cut-off of the continuous X-ray spectrum increases by a factor n = 3.0. Find the atomic number of the element of which the tube's anticathode is made.
What metal has in its absorption spectrum the difference between the frequencies of X-ray K and L absorption edges equal to ∆w = 6.85.1018 is s-1 ?
Calculate the binding energy of a K electron in vanadium whose L absorption edge has the wavelength λL = 2.4 nm.
Find the binding energy of an L electron in titanium if the wavelength difference between the first line of the K series and its short-wave cut-off is ∆λ = 26 pm.
Find the kinetic energy and the velocity of the photoelectrons liberated by Ks radiation of zinc from the K shell of iron whose K band absorption edge wavelength is λK = 174 pm.
Calculate the Lande g factor for atoms
(a) In S states;
(b) In singlet states.
Calculate the Lande g factor for the following terms:
(a) 6F1/2;
(b) 4DI/2;
(c) 5F2;
(d) 5P1;
(e) 3P0`
Calculate the magnetic moment of an atom (in Bohr magnetons)
(a) In 1F state;
(b) In 2D3/2 state;
(c) In the state in which S = 1, L = 2, and Lande factor g = 4/3.
Determine the spin angular momentum of an atom in the state D2 if the maximum value of the magnetic moment projection in that state is equal to four Bohr magnetons.
An atom in the state with quantum numbers L = 2, S = 1 is located in a weak magnetic field. Find its magnetic moment if the least possible angle between the angular momentum and the field direction is known to be equal to 30°.
A valence electron in a sodium atom is in the state with principal quantum number n = 3, with the total angular momentum being the greatest possible, what is its magnetic moment in that state?
An excited atom has the electronic configuration 1s22s22p3d being in the state with the greatest possible total angular momentum. Find the magnetic moment of the atom in that state.
Find the total angular momentum of an atom in the state with S = 3/2 and L = 2 if its magnetic moment is known to be equal to zero.
A certain atom is in the state in which S = 2, the total angular momentum M = √2h, and the magnetic moment is equal to zero. Write the spectral symbol of the corresponding term.
An atom in the state 2P3/2 is located in the external magnetic field of induction B = 1.0kG. In terms of the vector model find the angular precession velocity of the total angular momentum of that atom.
An atom in the state 2P1/2 is located on the axis of a loop of radius r = 5 cm carrying a current I = 10 A. The distance between the atom and the centre of the loop is equal to the radius of the latter. How great may be the maximum force that the magnetic field of that current exerts on the atom?
A hydrogen atom in the normal state is located at a distance r = 2.5 cm from a long straight conductor carrying a current I = 10 A. Find the force acting on the atom.
A narrow stream of vanadium atoms in the ground state 4F3/2 is passed through a transverse strongly inhomogeneous magnetic field of length l1 = 5.0 cm as in the Stern-Gerlach experiment. The beam splitting is observed on a screen located at a distance l2 = 15 cm from the magnet. The kinetic energy of the atoms is T = 22 MeV. At what value of the gradient of the magnetic field induction B is the distance between the extreme components of the split beam on the screen equal to δ = 2.0 mm?
Into what number of sublevels are the following terms split in a weak magnetic field:
(a) 3Po;
(b) 2F5/2;
(c) 4D1/2?
An atom is located in a magnetic field of induction B = - 2.50kG. Find the value of the total splitting of the following terms (expressed in eV units):
(a) 1D;
(b) 3F4.
What kind of Zeeman Effect normal or anomalous, is observed in a weak magnetic field in the case of spectral lines caused by the following transitions:
(a) 1P → 1S;
(b) 2D5/2 → 2P3/2;
(c) 3D1 → 3Po;
(d) 5I5 → 5H6?
Determine the spectral symbol of an atomic singlet term if the total splitting of that term in a weak magnetic field of induction B = 3.0kG amounts to ∆E = 104μV.
It is known that a spectral line λ = 612 nm of an atom is caused by a transition between singlet terms. Calculate the interval ∆λ between the extreme components of that line in the magnetic field with induction b = 10.0kG.
Find the minimum magnitude of the magnetic field induction B at which a spectral instrument with resolving power = 1.0.105 is capable of resolving the components of the spectral line λ = 536 nm caused by a transition between singlet terms. The observation line is at right angles to the magnetic field direction.
A spectral line caused by the transition 3D1 → 3P0 experiences the Zeeman splitting in a weak magnetic field. When observed at right angles to the magnetic field direction, the interval between the neighbouring components of the split line is ∆w = 1.32 ∙ 1010 s–1. Find the magnetic field induction B at the point where the source is located.
The wavelengths of the Na yellow doublet (2p → 2S) are equal to 589.59 and 589.00 nm. Find:
(a) The ratio of the intervals between neighbouring sublevels of the Zeeman splitting of the terms 2Pal 2 and 2Pal 2 in a weak magnetic field;
(b) The magnetic field induction B at which the interval between neighbouring sublevels of the Zeeman splitting of the term is η = 50 times smaller than the natural splitting of the term 2P.
Draw a diagram of permitted transitions between the terms 2P3/2 and 2S1/2 in a weak magnetic field. Find the displacements (in rad/s units) of Zeeman components of that line in a magnetic field B = 4.5kG.
The same spectral line undergoing anomalous Zeeman splitting is observed in direction 1 and, after reflection from the mirror M (Fig. 6.9), in direction 2. How many Zeeman components are observed in both directions if the spectral line is caused by the transition?
(a) 2P3/2 → 2S1/2;
(b) 3P2 → 3S1?
Calculate the total splitting ∆w of the spectral line 3D3 → 3P2 in a weak magnetic field with induction B = 3.4kG.
An alpha-particle with kinetic energy Ta = 7.0 MeV is scattered elastically by an initially stationary Li6 nucleus. Find the kinetic energy of the recoil nucleus if the angle of divergence of the two particles is O = 60°.
A neutron collides elastically with an initially stationary deuteron. Find the fraction of the kinetic energy lost by the neutron
(a) In a head-on collision;
(b) In scattering at right angles.
Find the greatest possible angle through which a deuteron is scattered as a result of elastic collision with an initially stationary proton.
Assuming the radius of a nucleus to be equal to R = 0.13 3√A pm, where A is its mass number, evaluate the density of nuclei and the number of nucleons per unit volume of the nucleus.
Write missing symbols, denoted by x, in the following nuclear reactions:
(a) B10 (x, a) Be8;
(b) 017 (d, n) x
(c) Na23 (p, x) Ne20;
(d) x (p, n) Ar 37.
Demonstrate that the binding energy of a nucleus with mass number A and charge Z can be found from Eq. (6.6b).
Find the binding energy of a nucleus consisting of equal numbers of protons and neutrons and having the radius one and a half times smaller than that of A127 nucleus.
Making use of the tables of atomic masses, find:
(a) The mean binding energy per one nucleon in 016 nucleuses
(b) The binding energy of a neutron and an alpha-particle in a B11 nucleus;
(c) The energy required for separation of an 016 nucleus into four identical particles.
Find the difference in binding energies of a neutron and a proton in a B11 nucleus. Explain why there is the difference.
Find the energy required for separation of a Ne20 nucleus into two alpha-particles and a C12 nucleus if it is known that the binding energies per one nucleon in Ne20, H4, and C12 nuclei are equal to 8.03, 7.07, and 7.68 MeV respectively.
Calculate in atomic mass units the mass of
(a) A Li8 s atom whose nucleus has the binding energy 4i.3 MeV;
(b) A C10 nucleus whose binding energy per nucleon is equal to 6.04 MeV.
The nuclei involved in the nuclear reaction A1 + A2 → A3 + A4 have the binding energies E1, E2, E3, and E4. Find the energy of this reaction.
Assuming that the splitting of a U235 nucleus liberates the energy of 200 MeV, find:
(a) The energy liberated in the fission of one kilogram of U isotope, and the mass of coal with calorific value of 30 kJ/g which is equivalent to that for one kg of U235;
(b) The mass of U 2as isotope split during the explosion of the atomic bomb with 30 kt trotyl equivalent if the calorific value of trotyl is 4.1kJ/g.
What amount of heat is liberated during the formation of one gram of He4 from deuterium He2? What mass of coal with calorific value of 30kJ/g is thermally equivalent to the magnitude obtained?
Taking the values of atomic masses from the tables, calculate the energy per nucleon which is liberated in the nuclear reaction Li6 + H2 → 2He4 Compare the obtained magnitude with the energy per nucleon liberated in the fission of U235 nucleus.
Find the energy of the reaction Li7+ p →2He4 if the binding energies per nucleon in Li7 and He4 nuclei are known to be equal to 5.60 and 7.06 MeV respectively.
Find the energy of the reaction N14 (a, p) O17 if the kinetic energy of the incoming alpha-particle is Ta 4.0 MeV and the proton outgoing at an angle 0 = 60 ° to the motion direction of the alpha-particle has a kinetic energy Tp = 2.09 MeV.
Making use of the tables of atomic masses, determine the energies of the following reactions:
(a) Li7 (p, n) Be7;
{b) Be9 (n, γ) Be10;
(c) Li7 (α, n) B10;
(d) 016 (d, α) N14.
Making use of the tables of atomic masses, find the velocity with which the products of the reaction B10 (n, α) Li7 come apart; the reaction proceeds via interaction of very slow neutrons with stationary boron nuclei.
Protons striking a stationary lithium target activate a reaction Li7 (p, n) Be7. At what value of the proton's kinetic energy can the resulting neutron be stationary?
An alpha particle with kinetic energy T = 5.3 MeV initiates a nuclear reaction Be9 (α, n) C12 la with energy yield Q = + 5.7 MeV. Find the kinetic energy of the neutron outgoing at right angles to the motion direction of the alpha-particle.
Protons with kinetic energy T = 1.0 MeV striking a lithium target induce a nuclear reaction p + Li7 → 2He4. Find the kinetic energy of each alpha-particle and the angle of their divergence provided their motion directions are symmetrical with respect to that of incoming protons.
A particle of mass m strikes a stationary nucleus of mass M and activates an endoergic reaction. Demonstrate that the threshold (minimal) kinetic energy required to initiate this reaction is defined by Eq. (6.6d).
What kinetic energy must a proton possess to split a deuteron H2 whose binding energy is Eb = 2.2MeV?
The irradiation of lithium and beryllium targets by a monoergic stream of protons reveals that the reaction Li7 (p, n) Be7 – 1.65MeV is initiated whereas the reaction Be9 (p, n) B9 – 1.85MeV does not take place. Find the possible values of kinetic energy of the protons.
To activate the reaction (n, a) with stationary B11 nuclei, neutrons must have the threshold kinetic energy Tth = 4.0MeV. Find the energy of this reaction.
Calculate the threshold kinetic energies of protons required to activate the reactions (p, n) and (p, d) with Li7 nuclei.
Using the tabular values of atomic masses, find the threshold kinetic energy of an alpha particle required to activate the nuclear reaction Li7 (a, n)B10. What is the velocity of the B10 nucleus in this case?
A neutron with kinetic energy T = 10 MeV activates a nuclear reaction C12 (n, α) Be9 whose threshold is Tth = 6.17 MeV. Find the kinetic energy of the alpha-particles outgoing at right angles to the incoming neutrons' direction.
How much, in per cent, does the threshold energy of gamma quantum exceed the binding energy of a deuteron (Eb = 2.2 MeV) in the reaction γ + H2 → n + p?
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