Question

The force constant of HF molecule is 970Nm-¹. Calculate the fundamental vibrational frequency as well as the zero point energy?
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Answer 1

Explanation:

Calculate the fundamental vibrational frequency and zero point energy. (Ans. 1.247 × 10−14) s−1, ...

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Answer 2

Given:

The force constant of HF molecule is 970 Nm-1

.

To find:

Calculate the fundamental vibrational  frequency as well as the zero-point energy.​

Solution:

From the given information, we have the data as follows.

The force constant of HF molecule is 970 Nm-1

.

⇒ K = 970 Nm-1

The fundamental vibrational  frequency is calculated as follows.

ν = 1/2π √[K / μ]

Here, μ = M/2

∴ ν = 1/2π √[2K / M]

Substitute the values in the above equation.

Here, M = 178.49 u

⇒ M = 178.49 × 1.6605 × 10^-27 kg

ν = 1/2π √[2 × 970 / (178.49 × 1.6605 × 10^-27)]

ν = 1.2876 × 10^{13} s^-1.

The zero point energy is calculated as follows.

ZPE = hν/2

Substitute the values in the above equation.

ZPE = (6.63 × 10^{-34} × 1.2876 × 10^{13} ) /2

ZPE = 4.2684 × 10^{-21} J.