Question

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

8.70 ×10⁴ m/s?

(b) At 1.40 × 10⁷ m/s?

Answer 1

Part a

Speed of electron u = 8.70 x 10^4 m/s

From de Broglie’s concept

- Plank’s constant =

- Mass of electron =

Wavelength of radiation

= (6.626 x 10^-34) / (9.11 x 10^-31 x 8.70 x 10^4)

= 8.36 x 10^-9 m

For any microscope,

smallest object that can be observed = 1/2 the wavelength of the radiation

smallest object observable with an electron microscope

= 8.36 x 10^-9 / 2

= 4.18 x 10^-9 m x 10^9 nm/m

= 4.18 nm

Part b

Speed of electron u = 1.40 x 10^7 m/s

From de Broglie’s concept

- Plank’s constant =

- Mass of electron =

Wavelength of radiation

= (6.626 x 10^-34) / (9.11 x 10^-31 x 1.40 x 10^7)

= 5.195 x 10^-11 m

For any microscope,

smallest object that can be observed = 1/2 the wavelength of the radiation

smallest object observable with an electron microscope

= 5.195 x 10^-11 / 2

= 2.598 x 10^-11 m x 10^9 nm/m

= 0.02598 nm