The force constant of HF molecule is 970 Nm^-1 . Calculate the fundamental vibrational frequency and zero point energy

To calculate the fundamental vibrational frequency and zero-point energy of the HF (hydrogen fluoride) molecule, we can use the quantum mechanical model of a harmonic oscillator. Here’s a step-by-step guide to solving the problem:

### 1. Fundamental Vibrational Frequency

The fundamental vibrational frequency (\(\nu\)) of a diatomic molecule like HF can be calculated using the formula:

\[
\nu = \frac{1}{2\pi} \sqrt{\frac{k}{\mu}}
\]

where:
- \( k = 970 \, \text{Nm}^{-1} \) is the force constant.
- \( \mu \) is the reduced mass of the HF molecule, given by:

\[
\mu = \frac{m_H \cdot m_F}{m_H + m_F}
\]

where \( m_H \) and \( m_F \) are the masses of the hydrogen and fluorine atoms, respectively.

Using the atomic masses:
- \( m_H = 1.00784 \, \text{u} \)
- \( m

The force constant of HF molecule is 970 Nm^-1. Calculate the fundamental vibrational frequency and zero point energy.

This guide explains how to calculate the fundamental vibrational frequency and zero-point energy for the HF molecule using quantum mechanics. With a force constant of 970 Nm^-1 and atomic masses for hydrogen and fluorine, we apply key formulas like the harmonic oscillator model. Suitable for undergraduate physics students.

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