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Answers to Chapter 24 problems

 

24.4.1   â€“0.0074 nm

24.4.2   1.2 × 1029 m;     6.3 × 1071 m

24.4.3   (a)  6.56 × 1012 Hz;   6.56 × 109 Hz;   6.56 × 106 Hz       (b)  7.67 × 1012 Hz;   6.64 × 109 Hz;   6.55 × 106 Hz 

24.4.4    25.64 nm

24.4.5    n = 8;    311 nm

24.4.6    He+  when  ni = 6, 8, 10, …. ;       ni = 7 to nf = 4

24.4.7   (a)  30.4 nm   (b)  292 nm   (c)  1.055 mm;      (a)  8.23 × 1014 Hz   (b)  3.66 × 1014 Hz   (c)  2.06 × 1014 Hz

24.4.8    1.05 × 105 K

24.4.9     1.094 × 106 m s−1;    5.15 × 1015 rad s−1;    1.22 × 10−15 s

24.4.10   9.107 × 10−31&²Ô²ú²õ±è;kg;    121.522 nm;    30.379 nm

24.4.11   E1 = −6.76 eV,  E2 = −1.69 eV;   6.76 eV;   244 nm 

24.4.12    1.69 x 10−28 kg;     2.51 keV;     2.98 x 10−13 m;     8.9 x 10−19 s  (this corresponds to 2.5 x 1012 orbits which can be completed in one muon lifetime so that the muonic atom can be considered to exist as a genuine bound system)

24.4.13    E/hf â‰ˆ 5.4 × 10−9.  For most purposes the correction for recoil is negligible.

24.4.14    \( { n^2 \hbar^2  \over m^2 GM} \);    n = 2.54 × 1074;      1.18 × 10−63 m

24.6.1   Maximum at r = 0.67a0 and 5.23a0;   Minimum at r = 0 and 2a0     (ii)  6a0

              

24.6.2   6.4 x 106

24.6.3   (i)  0.067     (ii)  0.175   (iii)  0.0135;    0.067 (This is the same as the (spherically symmetric {200} state) so that a determination of the probability distribution of electrons in the n = 2 state will yield the spherically symmetric average probability of the four (degenerate) n = 2 states and cannot be used to distinguish between them)

24.6.4   (i)  0.323     (ii)  0.439

24.6.5   (i)  \( <U> = -{ me^4 \over 16 \pi^2 {\epsilon_0}^2 \hbar^2} \)    (ii)  \( <K> = { me^4 \over 32 \pi^2 {\epsilon_0}^2 \hbar^2} \)    (c)  (i) + (ii) = \( -{ me^4 \over 32 \pi^2 {\epsilon_0}^2 \hbar^2} \) 

24.6.6   rmax = a0;   <r> = \( { 3 \over 2} \)a0 is greater than  rmax because P10(r) is not symmetric about its maximum 

24.6.7     \( { 1 \over a_0} \) ;    \( { 1 \over 4 a_0} \)

24.6.8    6.07 times

24.7.1   4f, 5p, 4p, 3p and 2p; 

             4f to 3d;  5p to 5s, 4s, 3s, 2s or 1s;  4p to 4s, 3s, 2s or 1s;  3p to 3s, 2s or 1s;  2p to 2s or 1s

24.7.2   An l = 1 (p) electron can only make transitions to l = 0 (s) or l = 2 (d) states

24.8.1  −3, −2, −1, 0, +1, +2, +3;       150°, 125.3°, 106.8°, 90°, 73.2°, 54.7° and 30°

24.9.1   1.7 × 10−5 eV

24.9.2   (a)  2.27 × 10−23 A m2    (b)  0.076 T

24.10.1   (a)  1.74 × 1012 m s&²Ô²ú²õ±è;−1 (almost four orders of magnitude greater than the velocity of light)

                (b)  5.8 x 10−13 m (a value which is considerably greater than the maximum radius of the electron)

                The classical model of electron spin does not stand up to close scrutiny; electron spin is not a classical concept

24.10.2    (a)  1.11 × 10−21 N      (b)  1.33 × 10−6 m

24.11.1    18 T 

 

24.11.2    2.3 × 10−5 eV (measured/fully quantum mechanical value is 4.6 × 10−5 eV).

24.13.1    group 0;   group Ia or Ib;   group III

24.13.2

24.13.3    −108.8 eV;   âˆ’68 eV;    30.5 nm (measured value is 58.4 nm)

24.13.4    1.5 eV

24.13.5    (i) 9.19 keV (observed value 8.33 keV);  0.135 nm   (ii) 110 keV (observed value 116 keV); 0.0113 nm

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