Hospital X-ray generators emit X-rays with wavelength of about 15.0 nanometers (nm), where 1nm = 10^-9m. What is the energy of the X-rays?
Express your answer to three significant figures and include the appropriate units.
Express your answer to three significant figures and include the appropriate units.
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We're dealing with photons here so this is best determined by use of quantum theory. The energy of a quanta of light is given by
E=hf
where h is Planck's (6.626x10^-34 kg m^2/s) constant and f is the frequency of light. The frequency of light is also given by v = c/L, where L is the wavelength of the light.
E = hc/L = (6.626x10^-34 kg m^2/s)(3.0x10^8 m/s)/(15x10^-9 m) = 1.33x10^-17 Joules or 82.7 eV.
We typically measure energy in units of eV (electron Volts) because of its simplicity in cgs units when we speak of relativistic quantum theory. This of course is not energetic enough for that theory but a joule is not particularly interesting as a unit.
E=hf
where h is Planck's (6.626x10^-34 kg m^2/s) constant and f is the frequency of light. The frequency of light is also given by v = c/L, where L is the wavelength of the light.
E = hc/L = (6.626x10^-34 kg m^2/s)(3.0x10^8 m/s)/(15x10^-9 m) = 1.33x10^-17 Joules or 82.7 eV.
We typically measure energy in units of eV (electron Volts) because of its simplicity in cgs units when we speak of relativistic quantum theory. This of course is not energetic enough for that theory but a joule is not particularly interesting as a unit.
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energy E = 12400 / 150 = 82.667 ev = 82.667 x1.6 x10^-19 J = 132.267 x10^-19 J
ie., E = 1.32267 x10^-17 J.
ie., E = 1.32267 x10^-17 J.