Be sure to answer all parts. An electron microscope focuses electrons through ma

Question

Be sure to answer all parts. An electron microscope focuses electrons through magnetic lenses to observe objects at higher magnification than is possible with a light microscope. For any microscope, the smallest object that can be observed is one-half the wavelength of the radiation used. Thus, for example, the smallest object that can be observed with light of 400.0 nm is 2.00 × 10-7 m. (a) What is the smallest object observable with an electron microscope using electrons moving at 7.10 × 104 m/s? × 10(select) (Enter your answer in scientific notation.) n (b) At 1.50 × 107 m/s? x 10 (selech m (Enter your answer in scientific notation.)

Explanation / Answer

Using the de Broglie's equation for matter waves: lambda = h/(mv)
We know that
h = Planck's constant = 6.63 x 10^-34 J.s
m = mass of an electron = 9.11 x 10^-31 kg

1.) lambda = h/(mv)
=>lambda = (6.63 x 10^-34 J.s)/ (9.11 x 10^-31 kg)(7.10 x 10^4 m/s) = 1.02 x 10 ^-8 m

=>9.58 x 10^-9 m/2 = 5.12x 10^-9 m

2) lambda = h/(mv)
=>lambda = (6.63 x 10^-34 J.s)/ (9.11 x 10^-31 kg)(1.50 x 10^7 m/s) = 4.85 x 10 ^-11m

=>4.85 x 10 ^-11 m/2 = 2.425x 10^-11 m

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