Rotational energy levels of diatomic molecules are well described by the formula E_(J)=BJ(J+1), where J is the rotational quantum number of the molecule and B its rotational constant. B is related to the reduced mass mu and the bond length R of the molecule through the equation B=h^(2)/(8pi^(2)muR^(2)). In general, spectroscopic transitions appear at photon energies which are equal to the energy difference between appropriate states of a molecule (hv=DeltaE). The observed rotational transitions occur between adjacent rotational levels, hence DeltaE=E_(J+1)-E_(J)=2B(J+1). Consequently, successive rotational transitions that appear on the spectrum (such as the one shown here) follow the equation h(Deltaupsilon)=2B. By inspecting the spectrum provided, determine the following quantities for ^(2) C ^(p)C with appropriate units (a) Deltaupsilon (b) B (c) R

Rotational energy levels of diatomic molecules are well described by t

1.	Rotational energy levels of diatomic molecules are well described by the formula E_(J)=BJ(J+1), where J is the rotational quantum number of the molecule and B its rotational constant. B is related to the reduced mass mu and the bond length R of the molecule through the equation B=h^(2)/(8pi^(2)muR^(2)). In general, spectroscopic transitions appear at photon energies which are equal to the energy difference between appropriate states of a molecule (hv=DeltaE). The observed rotational transitions occur between adjacent rotational levels, hence DeltaE=E_(J+1)-E_(J)=2B(J+1). Consequently, successive rotational transitions that appear on the spectrum (such as the one shown here) follow the equation h(Deltaupsilon)=2B. By inspecting the spectrum provided, determine the following quantities for ^(2) C ^(p)C with appropriate units (a) Deltaupsilon (b) B (c) R
Answer» Answer :{:a) For example : `DeltaV=1150-1035=115 GHz` {:b) `B=(hDeltav)/(2)=(6.63xx10^(-34)xx115'xx10^(9))/(2)=3.81xx10^(-23) J` {:c) `mu=(m(C)xxm(O))/(m(CO))=(12xx16)/(28)=6.86 a.u.=1,14 xx10^(-26) kg` For interatomic distance R: `R=(H)/(2pisqrt(2muB))=(3.63xx10^(-34))/(2xx3.14sqrt(2xx1.14xx10^(-26)xx3.81xx10^(-23)))=1.13xx10^(-10) m =1.13 Å`