Question

1. For each of the diatomic hydrides listed below, do the following: (a) For each hydride, calculate the force constant in centimetre-gram-second (CGS) units (b) For each hydride, calculate the bond length (in A) from the rotational constant. (c) Assuming the force constant does not change upon isotopic substitution, cal- culate the harmonic vibrational frequency, we, (in cm-) of the deuteride. (d) Assuming the bond length does not change upon isotopic substitution, calculate the rotational constant, B, (in cm1) of the deuteride. Molecule we (cm1) B (cm-1) LiH BeH BH CH NH OH HF 1405.65 2060.78 2366.90 2858.50 3282.27 16.699 3737.76 4138.32 20.956 7.513 10.314 12.021 14.457 18.911

Answer 1

Hi,

In the CGS units, frequency (cm^-1) and force constant k (erg/cm²) have the relation:

In the CGS units, frequency�v^-�(cm^-1) and force constant�k�(erg/cm^2) have the relation: v^- = 1/2 pi c squareroot k/mu where�c�is velocity of light in cm/sec and�mu�is reduced mass in gram. hence�k�can be calculated as: k = 4 pi^2 c^2 omega_e^2 mu rotational constant B(in cm-1) and bond length (r) have the relation: r = squareroot h/8 pi^2 c mu B Results are attached below: For the clarity, I have also attached the image of worksheet:

$\bar{\nu}= \frac{1}{2\pi c}\sqrt{\frac{k}{\mu}}$

where c is velocity of light in cm/sec and $\mu$ is reduced mass in gram.

hence k can be calculated as:

$k=4\pi^2c^2\omega_e^2\mu$

rotational constant B(in cm-1) and bond length (r) have the relation:

$B=\frac{h}{8\pi^2c\mu r^2}$

and r can be calculated in cm as:

$r=\sqrt{\frac{h}{8\pi^2c\mu B}}$

Results are attached below:

Molecule	?e (cm-1)	Reduced mass (a.u.)	Reduced mass (Grams)	k=4?2c2?2? erg-cm-2	Reduced mass of deuteride (a.u.)                         (gm)		?e (cm-1) of deuteride
LiH	1405.65	0.875	1.46125E-24	1.025E+05	1.556	2.5978E-24	1.054E+03
BeH	2060.78	0.900	1.503E-24	2.266E+05	1.636	2.7327E-24	1528.31535
BH	2366.9	0.917	1.53083E-24	3.044E+05	1.692	2.8262E-24	1741.99123
CH	2858.5	0.923	1.54154E-24	4.471E+05	1.714	2.8629E-24	2097.56554
NH	3282.27	0.933	1.55867E-24	5.960E+05	1.750	2.9225E-24	2397.03109
OH	3737.36	0.941	1.57176E-24	7.793E+05	1.778	2.9689E-24	2719.32883
HF	4138.32	0.950	1.5865E-24	9.644E+05	1.810	3.0219E-24	2998.49771
Molecule	B (cm-1)	Reduced mass (a.u.)	Grams	bond length (cm)	in Å	B' in cm-1 of deuteride
LiH	7.513	0.875	1.46125E-24	1.59706E-08	1.59706095	4.2260625
BeH	10.314	0.900	1.503E-24	1.34399E-08	1.3439942	5.6727
BH	12.021	0.917	1.53083E-24	1.23355E-08	1.2335484	6.511375
CH	14.457	0.923	1.54154E-24	1.12092E-08	1.12091885	7.78453846
NH	16.699	0.933	1.55867E-24	1.03721E-08	1.03721453	8.90613333
OH	18.911	0.941	1.57176E-24	9.70598E-09	0.97059809	10.0117059
HF	20.956	0.950	1.5865E-24	9.17733E-09	0.91773272	11.0019

For the clarity, I have also attached the image of worksheet:

Hope this resolves your problem.