6.46. Eb = Re4/2h2, R = µe4/2h3, where It is the reduced mass
of the system. If the motion of the nucleus is not taken into account,
these values (in the case of a hydrogen atom) are greater by m/M
0.055%, where m and M are the masses of an electron and a proton.
6.47. ED — EH = 3.7 meV,
— A.D = 33 pm.
6.48. (a) 0.285 pm, 2.53 keV, 0.65 nm; (b) 106 pm, 6.8 eV,
0.243 pm.
6.49. 123, 2.86 and 0.186 pm.
6.50. 0.45 keV.
6.51. For both particles X, = 27th (1 + mn/md)/r2ninT = 8.6 pm.
6.52. I= a1A,2/Y.24 + A.:.
6.53. X= 27th/ V 2mkT =128 pm.
6.54. First, let us find the distribution of molecules over de
Broglie wavelengths. From the relation f (v) dv =
(A.) where
f (v) is Maxwell's distribution of velocities, we obtain
q
= Ak-4e-a/12, a = 2n2h2/ n.kT.
The condition 41(14= 0 provides 47.= Tarr mkT = 0.09 nm.
6.55. X, = 2nh/V2m7' (1 -I- T/2mc2), T < 4mc2A?j1 = 20.4 keV (for
an electron) and 37.5 MeV (for a proton).
6.56. T = (j/2 1) mc2 = 0.21 MeV.
6.57.
Xonnil mcX.hlah= 3.3 pm.
6.58. v -=4rth//mbAx=-- 2.0-106 m/s.
6.59. Ax = 23-thlIdli2meT/ = 4.9 [tm.
6.60. Vo = n2h2/2rne (j/TI-1)2 d2 sin2 0 = 0.15 keV.
6.61. c/ = z-ak117 2mT cos (0/2) = 0.21 nm, where k= 4.
6.62. d= Takli 2mT sin 0 = 0.23 ± 0.04 nm, where k = 3 and the
angle 0 is determined by the formula tan 20 =D121.
6.63. (a) n= 111 +1/1/V= 1.05; (b) V/V i _.>-1/1 (2 -I-1) = 50.
6.64. En = n22-c2h2/2m12, where n = 1, 2, . . .
6.66. 1.104, 1.10 and 1.10-2° cm/s.
6.67. Au
-
hlml = 1.106 m/s; vi = 2.2.106 m/s.
6.69. At
▪
im/2/h
10-16 s.
6.70. Tmin h 2/2m12 = 1 eV. Here we assumed that p
Ap
and Ax = 1.
6.71. Av/v ti h//1/2mT = 1.10".
6.72. F
6.73. Taking into account that p Ap
Ax ,h1x, we get
E = T U h 2 /2mx2 kx 2/2. From the condition dEl dx = 0
we find x, and then Emin
klm = he), where co is the oscillator's angular frequency. The rigorous calculations furnish the value
ho /2.
6.74. Taking into account that p Ap
Ar and Ar r,
we get E = p2/2m — e2/r h2/2mr2 — e2/r. From the condition
of the system. If the motion of the nucleus is not taken into account,
these values (in the case of a hydrogen atom) are greater by m/M
0.055%, where m and M are the masses of an electron and a proton.
6.47. ED — EH = 3.7 meV,
— A.D = 33 pm.
6.48. (a) 0.285 pm, 2.53 keV, 0.65 nm; (b) 106 pm, 6.8 eV,
0.243 pm.
6.49. 123, 2.86 and 0.186 pm.
6.50. 0.45 keV.
6.51. For both particles X, = 27th (1 + mn/md)/r2ninT = 8.6 pm.
6.52. I= a1A,2/Y.24 + A.:.
6.53. X= 27th/ V 2mkT =128 pm.
6.54. First, let us find the distribution of molecules over de
Broglie wavelengths. From the relation f (v) dv =
(A.) where
f (v) is Maxwell's distribution of velocities, we obtain
q
= Ak-4e-a/12, a = 2n2h2/ n.kT.
The condition 41(14= 0 provides 47.= Tarr mkT = 0.09 nm.
6.55. X, = 2nh/V2m7' (1 -I- T/2mc2), T < 4mc2A?j1 = 20.4 keV (for
an electron) and 37.5 MeV (for a proton).
6.56. T = (j/2 1) mc2 = 0.21 MeV.
6.57.
Xonnil mcX.hlah= 3.3 pm.
6.58. v -=4rth//mbAx=-- 2.0-106 m/s.
6.59. Ax = 23-thlIdli2meT/ = 4.9 [tm.
6.60. Vo = n2h2/2rne (j/TI-1)2 d2 sin2 0 = 0.15 keV.
6.61. c/ = z-ak117 2mT cos (0/2) = 0.21 nm, where k= 4.
6.62. d= Takli 2mT sin 0 = 0.23 ± 0.04 nm, where k = 3 and the
angle 0 is determined by the formula tan 20 =D121.
6.63. (a) n= 111 +1/1/V= 1.05; (b) V/V i _.>-1/1 (2 -I-1) = 50.
6.64. En = n22-c2h2/2m12, where n = 1, 2, . . .
6.66. 1.104, 1.10 and 1.10-2° cm/s.
6.67. Au
-
hlml = 1.106 m/s; vi = 2.2.106 m/s.
6.69. At
▪
im/2/h
10-16 s.
6.70. Tmin h 2/2m12 = 1 eV. Here we assumed that p
Ap
and Ax = 1.
6.71. Av/v ti h//1/2mT = 1.10".
6.72. F
6.73. Taking into account that p Ap
Ax ,h1x, we get
E = T U h 2 /2mx2 kx 2/2. From the condition dEl dx = 0
we find x, and then Emin
klm = he), where co is the oscillator's angular frequency. The rigorous calculations furnish the value
ho /2.
6.74. Taking into account that p Ap
Ar and Ar r,
we get E = p2/2m — e2/r h2/2mr2 — e2/r. From the condition