A vibrating mass-spring system has a frequency of 0.56 Hz. How much energy of this vibration is carried away in a one-quantum change?

1 Answer
Truong-Son N.
Jun 30, 2017

Well, one quantum, i.e. the energy for one photon, is given by #hnu#, where #h# is Planck's constant and #nu# is the frequency in #"s"^(-1)#.

We don't even really need to know that it's a harmonic oscillator system to know that the energy the system loses into its surroundings by extracting one quantum of energy is

#color(blue)(E_"lost") = hnu#

#= (6.626 xx 10^(-34) "J"cdot"s")("0.56 s"^-1) = color(blue)(3.7 xx 10^(-34) "J")#

And this is sensibly small.

Quantum mechanics literally applies to particles on the order of #10^(-10)# #"m"# or so (which is why the angstrom is often used in quantum chemistry; an angstrom is #10^(-10)# #"m"#).

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