Question

In rotational energy levels of co molecule, lo to
1-2 absorbtion line occurs at Frequency 115 x 10142
If the reduced mass of the co molecule is
1-14 x 10-25 kg, Find the interatomic distance
betwee C & o
(Arr. 1.13A)
atoms​

Answer 1

Answer:

Explanation:

Is the bond length in HBr the same as that in DBr? The wavenumbers of the J=1←0 rotational transitions for H79Br and 2H79Br are 16.68467 and 8.48572 cm-1, respectively. Atomic masses are 1.007825 u and 2.0140 u for 1H and 2H, respectively. The mass of 79Br is 78.91833 u. Is there a difference in bond lengths between these two molecules?

S12.8

Given that:

R2=ℏ4πcμB(12.E.11)

B=ℏ4πcI(12.E.12)

I=μR2(12.E.13)

We find the following values:

ℏ4πc=2.79927×10−44kg⋅m(12.E.14)

μ(HBr)=(1.007825u×78.91833u1.007825u+78.91833u)×(1.66054×10−27kg⋅u−1)=0.995117×10−27kg(12.E.15)

μ(DBr)=(2.0140u×78.91833u2.0140u+78.91833u)×(1.66054×10−27kg⋅u−1)=1.96388×10−27kg(12.E.16)

We then solve for the bond lengths:

R2(HBr)=(2.79927×10−44kg⋅m)(0.995117×10−27kg)(1.668467×103m−1)=1.6860×10−20pm2(12.E.17)

R(HBr)=129.85pm(12.E.18)

R2(DBr)=(2.79927×10−44kg⋅m)(1.96388×10−27kg) (8.48572×102m−1)=1.6797×10−20pm2(12.E.19)

R(DBr)=129.60pm(12.E.20)

Yes, there exists a small difference between the bond lengths of H79Br and D79Br.