Question

For any microscope, the size of the smallest observable object is one-half the wavelength of the radiation used. For example, the smallest object observable with 400-nm light is 2X10⁻⁷ m.
(a) What is the smallest observable object for an electron microscope using electrons moving at 5.5X10⁴ m/s?

Answer 1

The smallest observable object for an electron microscope is 6.6nm.

Calculation of smallest observable object for an electron microscope :

Given,

Speed of electron (u) = 5.5 x 10⁴ m/s

De Broglie's formula,

wavelength, λ =h/mu

where,  

h = Planck's constant = 6.626 x $10^{-34}$ Js

m = mass of electron, 9.11 x $10^{-31}$ kg

λ =h/mu

= 6.626 x $10^{-34}$ Js /9.11 x $10^{-31}$ kg x 5.5 x 10⁴ m/s

= 0.132 x $10^{-7}$ m

= 13.2 x $10^{-9}$ m

It is well known that the smallest thing that can be observed under any microscope is identical to the radiation's wavelength for the smallest object that can be seen under an electron microscope.

Therefore, 13.2 x $10^{-9}$ m/2

= 6.6 x $10^{-9}$ m

= 6.6 nm

Hence, the smallest observable object for an electron microscope is 6.6nm.

Learn more about electron microscope here:

brainly.com/question/13884997

#SPJ4