Question

The difference in energy between allowed oscillator states in HBr molecules is 0.0330eV. What is the oscillation frequency of this molecule?

Short answer

The oscillation frequency of the molecule f= 8.00 × 10¹³ Hz.

Step-by-step solution

Oscillation frequency of the molecule

From the equation, the energy of an oscillator having a frequency of fisgiven by

\[E=\left({n+\frac{1}{2}}\right)hf\]

...(1)

Where n = 0,1,2,3,……. is any non-negative integer

h =6.626 ×10^-34 Js is Planck's constant. }

Now, from the equation, only those states of an oscillator are allowed for which their energy increase or decreases only in discrete steps of size

∆E =hf ...(2)

Here the difference in energy between allowed oscillator states in HBr molecules is

∆E= 0.330eV

Solve the equation

As we know

1.00 J = 0.625 × 10¹⁹ eV

So we get

\begin{aligned}\Delta E=0.330\,{\rm{eV}}\times\frac{{1.00\,{\rm{J}}}}{{0.625\times{{10}^{19}}\,{\rm{eV}}}}\\ = 0.528 \times {10^{ - 19}}\,{\rm{J}}\end{aligned}

Substitute all the values in the above equation (2), and we get

\begin{aligned}f=\frac{{\Delta E}}{h}\\=\frac{{0.528\times{{10}^{-19}}\,{\rm{J}}}}{{6.626\times{{10}^{-34}}\,{\rm{Js}}}}\\=7.9686\times{10^{13}}\,{\rm{Hz}}\\=8.00\times{10^{13}}\,{\rm{Hz}}\end{aligned}

Hence, f =8.00 ×10¹³Hz.