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where a is the correction constant which is equal to unity for light elements.
- Magnetic moment of an atom and Lande g^ factor:
g J (J + 1) g —1+
J (1-1-1)+S (S+1)—L(L+1) (6.3g) 2J (J -{-1)
- Zeeman splitting of spectral lines in a weak magnetic field: MI) = (rnigi— m 2g2) tI BBM. (6.3h)
- With radiation directed along the magnetic field, the Zeeman compo- nents caused by the transition m1= m2are absent.
6.97. 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. 6.98. 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. 6.99. 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 X = 813 nm and the short-wave cutoff wavelength of that series to X2= 350 nm. 6.100. 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. 6.101. 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. 6.102. The first line of the sharp series of atomic cesium is a doub- let 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. 6.103. Write the spectral designations of the terms of the hydrogen atom whose electron is in the state with principal quantum number n = 3. 6.104. 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? 6.105. Find the possible values of total angular momenta of atoms in the states 4P and 6D. 6.106. 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. 6.107. 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.
17*
6.108. An atom is in the state whose multiplicity is three and the total angular momentum is (^) hi/ 20. What can the corresponding quantum number L be equal to? 6.109. Find the possible multiplicities x of the terms of the types (a) "D2; (b) HP3/2; (c) 'F1. 6.110. 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. 6.111. An atom possessing the total angular momentum I Y 6 is in the state with spin quantum number S = 1. In the correspond- ing vector model the angle between the spin momentum and the total angular momentum is 0 = 73.2°. Write the spectral symbol for the term of that state. 6.112. Write the spectral symbols for the terms of a two-electron system consisting of one p electron and one d electron. 6.113. A system comprises an atom in 2P3/2state and a d electron. Find the possible spectral terms of that system. 6.114. Find out which of the following transitions are forbidden by the selection rules: (^2) D312 2P112, 3P1 2S172, 3F^3 3p 2, 4F71 2 4D 512. 6.115. Determine the overall degeneracy of a 3D state of a Li atom. What is the physical meaning of that value? 6.116. Find the degeneracy of the states 2P, 3D, and 4F possessing the greatest possible values of the total angular momentum. 6.117. 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. 6.118. What element has the atom whose K, L, and M shells and 4s subshell are filled completely and 4p subshell is half-filled? 6.119. Using the Hund rules, find the basic term of the atom whose partially filled subshell contains (a) three p electrons; (b) four p electrons. 6.120. Using the Hund rules, find the total angular momentum of the atom in the ground state whose partially filled subshell contains (a) three d electrons; (b) seven d electrons. 6.121. Making use of the Hund rules, find the number of electrons in the only partially filled subshell of the atom whose basic term is (a) 3F2; (b) 2P312; (c) 685/2. 6.122. Using the Hund rules, write the spectral symbol of the basic term of the atom whose only partially filled subshell (a) is filled by 1/3, and S = 1; (b) is filled by 70%, and S = 3/2. 6.123. The only partially filled subshell of a certain atom contains three electrons, the basic term of the atom having L = 3. Using
(b) the difference in binding energies of K and L electrons in
vanadium. 6.135. How many elements are there in a row between those whose wavelengths of Kalines are equal to 250 and 179 pm? 6.136. Find the voltage applied to an X-ray tube with nickel
anticathode if the wavelength difference between the K c, line and
the short-wave cut-off of the continuous X-ray spectrum is equal to 84 pm. 6.137. At a certain voltage applied to an X-ray tube with alumi- nium anticathode the short-wave cut-off wavelength of the contin-
uous 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? 6.138. When the voltage applied to an X-ray tube increased from
V1 = 10 kV to V , = 20 kV, the wavelength interval between
the Kaline 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. 6.139. What metal has in its absorption spectrum the difference
between the frequencies of X-ray K and L absorption edges equal
to Au) = 6.85.1018 s-1?
6.140. Calculate the binding energy of a K electron in vanadium
whose L absorption edge has the wavelength X, = 2.4 nm.
6.141. 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 A? = 26 pm. 6.142. Find the kinetic energy and the velocity of the photoelect-
rons liberated by Kc, radiation of zinc from the K shell of iron whose
K band absorption edge wavelength is ?K = 174 pm.
6.143. Calculate the Lande g factor for atoms
(a) in S states; (b) in singlet states.
6.144. Calculate the Lande g^ factor for the following terms:
(a) 6F1/2; (b) 4D112; (c) 5F2; (d) 5P1; (e) 3Po. 6.145. Calculate the magnetic moment of an atom (in Bohr magnetons)
(a) in 1 F state;
(b) in 2D312state;
(c) in the state in which S = 1, L =^ 2, and Lande factor^ g =^ 4/3.
6.146. Determine the spin angular momentum of an atom in the state D2 if the maximum value of the magnetic moment pro- jection in that state is equal to four Bohr magnetons.
6.147. 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°. 6.148. 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?
6.149. 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. 6.150. 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.
6.151. A certain atom is in the state in which S = 2, the total
angular momentum M = V 2h , and the magnetic moment is equal
to zero. Write the spectral symbol of the corresponding term. 6.152. An atom in the state 2P312is located in the external magne-
tic field of induction B = 1.0 kG. In terms of the vector model find
the angular precession velocity of the total angular momentum of that atom. 6.153. An atom in the state 2P,12is located on the axis of a loop
of radius r = 5 cm carrying a current I = 10 A. The distance be-
tween 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? 6.154. 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.
6.155. A narrow stream of vanadium atoms in the ground state 4 F312is passed through a transverse strongly inhomogeneous magnet-
ic field of length 1, =^ 5.0 cm as in the Stern-Gerlach experiment.
The beam splitting is observed on a screen located at a distance /2= 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 6 = 2.0 mm? 6.156. Into what number of sublevels are the following terms split in a weak magnetic field: (a) 3P0; (b) 2F512; (c) 4P1/2?
6.157. An atom is located in a magnetic field of induction B
= 2.50 kG. Find the value of the total splitting of the following
terms (expressed in eV units): (a) 1D; (b) 3F4. 6.158. 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) (^113) (b) 2D512 -* 2P312; (c)3D1 -* 3P0; (d) 5/5 (^) 5H4? 6.159. Determine the spectral symbol of an atomic singlet term if the total splitting of that term in a weak magnetic field of induc-
tion B = 3.0 kG amounts to AE = 104 ['RV.
6.160. It is known that a spectral line = 612 nm of an atom is caused by a transition between singlet terms. Calculate the inter- val AX, between the extreme components of that line in the magnetic
field with induction B = 10.0 kG.
