Discussion
A typical PR contour for vibration-rotational spectrum for CO molecule shows \(\Delta\bar{\nu}\) = 55 cm\(^{-1}\). The associated value of rotational constant B is (Given; Boltzmann const. k = 1.38 × 10\(^{-23}\) J/K, T = 300, h = 6.6 × 10\(^{-34}\) J-s) :
Answer: A
The rotational constant is about 1.8 cm\(^{-1}\).
In a vibration-rotation band the most intense lines of the P and R branches come from \(J_{max} \approx \sqrt{kT/2hcB}\), and the separation between the two maxima is about \(4BJ_{max}\):
\[ \begin{aligned} \Delta\bar{\nu} &= \sqrt{\frac{8BkT}{hc}} \\ B &= \frac{hc(\Delta\bar{\nu})^{2}}{8kT} \end{aligned} \]
With c in cm/s:
\[ \begin{aligned} \frac{hc}{kT} &= \frac{(6.6 \times 10^{-34})(3 \times 10^{10})}{1.38 \times 10^{-23} \times 300} \\ &\approx 4.78 \times 10^{-3}\ \text{cm} \end{aligned} \]
\[ \begin{aligned} B &= \frac{4.78 \times 10^{-3} \times 55^{2}}{8} \\ &= \frac{14.5}{8} \approx 1.8\ \text{cm}^{-1} \end{aligned} \]
This is close to the known value for CO (about 1.9 cm\(^{-1}\)). The other options do not follow from the given separation.
Post your comment
Please log in or register to post a comment.
Examination Categories
- SSC Exams
- Banking Exams
- Teaching Exams
- Civil Services Exams
- Railways Exams
- Engineering Recruitment Exams
- Defence Exams
- State Government Exams
- Police Exams
- Insurance Exams
- Nursing Exams
- Other Government Exams
- NRA CET
- PG Entrance Exams
- Campus Placement
- MBA Entrance Exams
- CUET and UG Entrance
- Judiciary Exams
- Regulatory Body Exams
- Software Development