Question

Constanta Part A If you use light of this wavelength, what would be the energy (in eV) of a single photon? To investigate the structure of extremely small objects, such as viruses, the wavelength of the probing wave should be about one-tenth the size of the object for sharp images. But as the wavelength gets shorter, the energy of a photon of light gets greater and could damage or destroy the object being studied. One alternative is to use electron matter waves instead of light. Viruses vary considerably in size, but 50.0 mm is not unusual. Suppose you want to study such a virus, using a wave of wavelength 5.00 mm You may want to review (Pages 919 - 921). For related problem-solving tips and strategies, you may want to view a Video Tutor Solution of Electron wavelengths. 96 AED ? eV Submit Request Answer Part B If you use an electron of this wavelength, what would be its kinetic energy (in eV)? V AXD + ? Submit Request Answer Part C Is it now clear why matter waves (such as in the clectron microscope) are often preferable to clectromagnetic waves for studying microscopic objects?

Answer 1

ev 1.60 X 10-19 h = 6.63 X 10-34 IJs A) Energy of phoon is given by hc Epheten = c = 2.99 X10 m/s & Given = 5:00 nm 2 5.00 X10-9, : Ephoton 6.63X10-34J-s X2.99x100 mls 5.00 X 10-9 m Ephoton = 3.96474 x 10-17 J Ephoton 3.96474 X10-17 J 1.60X10-19 olev (Ephoton = 2.48 x 10² eV B ) Using De Broglie equation h mu = h sla -34 J-S, h = 6.63810 9.11 X 10-31 Kg 6.63X10-34 J.S d = 5.00 x10-9 (mass of election) V 31 9.11 X 100 Kg X 5.000 10-9

Kinetic 1.45554 X105 ms energy of electron Ke = // mv² x 9.11x10-31 kg x (1.45554 x105m/s)? Ke -24 = 9.650207 X10 J 9.650207 X10-24J 1.60 X10-19 Jlev = 6:03 X10-5ev Ke o for same wavelength kinetic energy of electron, ke (6.03610-8 eu) is much less than the energy of photon , Ephoton (2148 x10?ev). Hemce damage to the object under observation using elechon beam is less likely compared to that of using light for same resolution. This is why matter waves are preferable to electromagnetic wares for studying microscopic objects.