To solve, use the formula of energy level of harmonic oscillator.
`E_n = (n + 1/2)hf`
where
`E_n` is the energy level of harmonic oscillator in Joules
n is the quantum level
h is the Planck's constant `(6.623 xx 10^(-34) Js)`
and f is the frequency of oscillator.
To be able to apply this formula, convert the given energy to Joules. Take note that `1eV = 1.602xx10^(-19)J` .
`E_n=5.45 eV * (1.602xx10^(-19)J)/(1eV)`
`E_n = 8.7309xx10^(-19)...
To solve, use the formula of energy level of harmonic oscillator.
`E_n = (n + 1/2)hf`
where
`E_n` is the energy level of harmonic oscillator in Joules
n is the quantum level
h is the Planck's constant `(6.623 xx 10^(-34) Js)`
and f is the frequency of oscillator.
To be able to apply this formula, convert the given energy to Joules. Take note that `1eV = 1.602xx10^(-19)J` .
`E_n=5.45 eV * (1.602xx10^(-19)J)/(1eV)`
`E_n = 8.7309xx10^(-19) J`
Plug-in this value of En to the formula of energy level of harmonic oscillator.
`E_n = (n+1/2)hf`
`8.8309 xx10^(-19) J= (3+1/2)(6.623 xx 10^(-34) Js)f`
`8.7309 xx10^(-19) J=(2.31805 xx10^(-33) Js) f`
Then, isolate the f.
`f = (8.7309 xx 10^(-19)J)/(2.31805xx10^(-33)Js)`
`f=3.76648476xx10^14``/ sec`
`f=3.76648476 xx 10^14Hz`
So the frequency of the oscillator is `3.76648476xx10^14Hz` .
To determine the angular frequency, apply the formula:
`omega = 2pif`
`omega =2pi * (3.76648476xx10^14 Hz)`
`omega=2.366552170 xx10^15` rad/s
Rounding off to two decimal places, it becomes:
`omega =2.37 xx10^15` rad/s
Therefore, the angular frequency of harmonic oscillator is `2.37xx10^15` radian per second.
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