MCAT General Chemistry Question 257: Answer and Explanation

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Question: 257

6. For a diatomic molecule, the reduced mass is given by u = (m₁ × m₂) / (m₁ + m₂) where m₁ and m₂ are the atomic weights of the two bonded atoms. What will be the ratio of the ground state vibration energies of D₂ to H₂ assuming the force constant k is the same for both?

A. 0.5
B. 0.7
C. 1.4
D. 2.0

Correct Answer: B

Explanation:

B Deuterium (D) has one proton, one neutron, and an atomic mass of 2. For D₂, u = (2 × 2) / (2 + 2) = 1. For H₂, u = 1 × 1 / (1 + 1) = 1/2. Since v, h, and k are all constant in this comparison, the vibration energy equation in the passage reduces as follows:

The ratio of this energy for D₂ to H₂ is:

The quantity must be greater than 0.5 but less than 1, so only choice B is possible.

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