Answer to Question #156372 in Physics for Janine

Question

A scanning electron microscope is operating with 25 keV electrons.

a) Calculate the energy, in J, possessed by the electrons (2 marks)

b) Calculate the velocity of the electron, given that the mass of an

electron is 9.11 × 10-31 kg (2 marks)

c) Calculate the momentum of the electrons (2 marks)

d) Hence calculate the wavelength of the electrons (2 marks)

e) What effect would increasing the electron energy have on the

wavelength, and what consequence would that have on the resolution of the images? (2 marks)

In ultrasound, increasing the frequency improves the resolution of the image but,

f) what happens to the depth of the scan that you can obtain when the frequency is increased?

Answer 1

a) Calculate the energy in J.

1 keV is 1000 eV, and 1 eV is equal by magnitude to the charge of an electron:

$$25\text{ keV}\equiv25\cdot1000\cdot1.609\cdot10^{-19}=4\cdot10^{-15}\text{ J}.$$

b) The velocity of an electron can be found from its energy:

$$v=\sqrt{\frac{2E_k}{m_e}}=93.78\cdot10^6\text{ m/s}.$$

c) The momentum is

$$p=m_ev=8.54\cdot10^{-23}\text{ kg m/s}.$$

d) The wavelength is

$$\lambda=\frac{h}{p}=7.76\cdot10^{-12}\text{ m}.$$

e) Increasing the energy decreases the wavelength and increases the resolution of the image.

f) The depth of scan increases with decreasing wavelengths.