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The correct order of the fundamental vibrational frequencies of the following diatomic molecules is
- a)1H35Cl > 1H37Cl > 2D35Cl
- b)2D35Cl > 1H37Cl > 1H35Cl
- c)1H37Cl > 1H35Cl > 2D35Cl
- d)1H37Cl > 2D35Cl > 1H35Cl
Correct answer is option 'A'. Can you explain this answer?
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Explanation:
To determine the correct order of the fundamental vibrational frequencies of the diatomic molecules, we need to consider the isotopes and their respective masses. The vibrational frequency is inversely proportional to the reduced mass of the molecule.
1H35Cl:
This molecule consists of hydrogen-1 (proton) and chlorine-35 (isotope with atomic mass 35). The reduced mass of this molecule can be calculated as follows:
Reduced mass = (Mass of hydrogen-1 * Mass of chlorine-35) / (Mass of hydrogen-1 + Mass of chlorine-35)
= (1 * 35) / (1 + 35)
= 35/36
1H37Cl:
This molecule consists of hydrogen-1 (proton) and chlorine-37 (isotope with atomic mass 37). The reduced mass of this molecule can be calculated as follows:
Reduced mass = (Mass of hydrogen-1 * Mass of chlorine-37) / (Mass of hydrogen-1 + Mass of chlorine-37)
= (1 * 37) / (1 + 37)
= 37/38
2D35Cl:
This molecule consists of deuterium-2 (isotope of hydrogen with atomic mass 2) and chlorine-35. The reduced mass of this molecule can be calculated as follows:
Reduced mass = (Mass of deuterium-2 * Mass of chlorine-35) / (Mass of deuterium-2 + Mass of chlorine-35)
= (2 * 35) / (2 + 35)
= 70/37
Based on the calculations above, we can compare the reduced masses of the molecules to determine their vibrational frequencies. The molecule with the lowest reduced mass will have the highest vibrational frequency.
Comparing the reduced masses:
1H35Cl: 35/36
1H37Cl: 37/38
2D35Cl: 70/37
The reduced mass in ascending order is:
1H35Cl < 1h37cl="" />< />
Therefore, the correct order of the fundamental vibrational frequencies of the diatomic molecules is:
1H35Cl < 1h37cl="" />< />
Answer: Option A
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