Is it now clear why matter waves (such as inthe electron microscope) are often p

Question

Is it now clear why matter waves (such as inthe electron microscope) are often preferable to electromagneticwaves for studying microscopic objects? To investigate the structure of extremely small objects, such asviruses, the wavelength of the probing wave should be aboutone-tenth the size of the object for sharp images. But as thewavelength gets shorter, the energy of a photon of light getsgreater and could damage or destroy the object being studied. Onealternative is to use electron matter waves instead of light.Viruses vary considerably in size, but 50.0 nm is not unusual. Suppose youwant to study such a virus, using a wave of wavelength5.00 nm. If you use light of this wavelength, what would be the energy (in eV) of a single photon? If you use an electron of this wavelength, what would be itskinetic energy (in eV)? Is it now clear why matter waves (such as inthe electron microscope) are often preferable to electromagneticwaves for studying microscopic objects?

Explanation / Answer

Energy of a photon can be expressed in terms of its wavelength as: E = hc/ So, in eV, E = (hc)/(e) =(6.636*10-34*3*108)/(1.602*10-19*5*10-9)eV                     = 248.539 eV For an electron, De-Broglie's equation tells us that : = h/mv So, E = mv2/2 = h2/2em2 So, E(electron) = 6.041 eV Thus, electrons of identical wavelength have far less energy ascompared to photons, and are better suited for suchinvestigations.

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