Only three lines observed R(0) R(1) P(1) The detection of R(1) and P(1) indicates T> 0K Harry Kroto 2004

Only three lines observed R(0) R(1) P(1) The detection of R(1) and P(1) indicates T> 0K  l  Io I I I = Ioe- l I = Io (1 - l + …) Io - I = I ~ l Harry Kroto 2004

IR(1) /IR(0) ~ R(1) /R(0) Only three lines observed R(0) R(1) P(1) The detection of R(1) and P(1) indicates T> 0K  l  Io I I I = Ioe- l I = Io (1 - l + …) (Io – I)/ Io = I/ Io ~ l IR(1) /IR(0) ~ R(1) /R(0) Harry Kroto 2004

IR(1) /IR(0) ~ R(1) /R(0) Only three lines observed R(0) R(1) P(1) The detection of R(1) and P(1) indicates T> 0K  l  Io I I I = Ioe- l I = Io (1 - l + …) (Io – I)/ Io = I/ Io ~ l IR(1) /IR(0) ~ R(1) /R(0) Harry Kroto 2004

IR(1) /IR(0) ~ R(1) /R(0) Only three lines observed R(0) R(1) P(1) The detection of R(1) and P(1) indicates T> 0K  l  Io I I I = Ioe- l I = Io (1 - l + …) (Io – I)/ Io = I/ Io ~ l IR(1) /IR(0) ~ R(1) /R(0) Harry Kroto 2004

IR(1) /IR(0) ~ R(1) /R(0) Only three lines observed R(0) R(1) P(1) The detection of R(1) and P(1) indicates T> 0K  l  Io I I I = Ioe- l I = Io (1 - l + …) (Io – I)/ Io = I/ Io ~ l IR(1) /IR(0) ~ R(1) /R(0) Harry Kroto 2004

Fermi’s Golden Rule x Io I l Harry Kroto 2004

Beer Lambert Law I= Io e-l Fermi’s Golden Rule x Io I l Beer Lambert Law I= Io e-l Harry Kroto 2004

Beer Lambert Law I= Io e-l Fermi’s Golden Rule x Io I l Beer Lambert Law I= Io e-l Harry Kroto 2004

Beer Lambert Law I= Io e-l Fermi’s Golden Rule x Io I l Beer Lambert Law I= Io e-l Harry Kroto 2004

Beer Lambert law I= Io e-l Fermi’s Golden Rule x Io I l Beer Lambert law I= Io e-l Harry Kroto 2004

Beer Lambert law I= Io e-l  is the absorption coefficient Fermi’s Golden Rule x Io I l Beer Lambert law I= Io e-l  is the absorption coefficient  = (83/3hc)n em 2 (Nm-Nn)(o-) Harry Kroto 2004

 = (4/3ħc) n em2  (Nm-Nn) (o-) Harry Kroto 2004

 = (4/3ħc) n em2  (Nm-Nn) (o-) ① Square of the transition moment n em2 Harry Kroto 2004

 = (4/3ħc) n em2  (Nm-Nn) (o-) ① ② Square of the transition moment n em2 Frequency of the light  Harry Kroto 2004

 = (4/3ħc) n em2  (Nm-Nn) (o-) ① ② ③ Square of the transition moment n em2 Frequency of the light  Population difference (Nm- Nn) Harry Kroto 2004

 = (4/3ħc) n em2  (Nm-Nn) (o-) ① ② ③ ④ Square of the transition moment n em2 Frequency of the light  Population difference (Nm- Nn) Resonance factor - Dirac delta function (0) = 1 Harry Kroto 2004

C Solution > Energy Levels For the H atom we shall just use the Bohr result E(n) = - R/n2 D Selection Rules n no restriction l = ±1 E Transition Frequencies E = - R[ 1/n22 – 1/n12] Harry Kroto 2004

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Hot gas cloud –the famous Orion Nebulae At the centre is the Trapezium Cluster of very hot new stars Harry Kroto 2004

2b = 103/n yrs per collision 3b = 1023/n2 yrs per collision Collisions in the Interstellat Medium ISM In space the pressures are low Very low If n = number of molecules per cc (mainly H) then 2b = 103/n yrs per collision 3b = 1023/n2 yrs per collision Number densities are anything from n = 1-1000 Harry Kroto 2004

Einstein Coefficients Bn<-m m Harry Kroto 2004

Einstein Coefficients Bn<-m Bn->m m Harry Kroto 2004

An->m/ Bn->m = 8h3/c 3 Einstein Coefficients n Bn<-m Bn->m An->m m An->m/ Bn->m = 8h3/c 3 Harry Kroto 2004

Einstein Coefficients Bn<-m Bn->m An->m m A = 1.2 x 10-37 3 n em2 transitions per sec Spontaneous emission lifetime   (sec) = 1/A = 1037/3 sec Harry Kroto 2004

 (sec) = 1037/3   (cm-1)  (Hz) 3 (Hz3)  (sec) H (1420 MHz) 21cm 0.05 1.5x109 3x1027 1010 * H2CO rotations 1cm 1 3 x 1010 3x1031 106 CO2 vibrations 10 103 3 x 1013 3 x 1040 10-3 Na D electronic 500nm 2x104 1.5 x 1014 6 x 1044 10-7 H Lyman  100nm 105 3 x 1015 3 x 1046 10-9 Calculations assume e = 1Debye 1yr = 3 x 107 sec * magnetic dipole Harry Kroto 2004

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Bohr radius an = aon2 ao = 0.05 nm Harry Kroto 2004

Bohr radius an = aon2 ao = 0.05 nm Calculate a10, a100 and a300 in cm Harry Kroto 2004

Bohr radius an = aon2 ao = 0.5 Å (1Å = 10-8cm) a300 = 0.5x10-3 cm = 0.005 mm Harry Kroto 2004

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Nitrosoethane Harry Kroto 2004

What can molecules do Harry Kroto 2004

What can molecules do 2 Harry Kroto 2004

What can molecules do 2 Harry Kroto 2004

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