Question

In an electron microscope, electrons are accelerated through a potential difference of 200 kV. What is the best possible resolution of the microscope?

Hint:

The de Broglie wavelength is crucial for determining the resolution of electron microscopes. A higher acceleration (voltage) results in shorter wavelengths and better resolution.

Answer 1

Correct Answer: 2.3

Step 1: Calculate the electron's de Broglie wavelength.
The de Broglie wavelength \( \lambda \) of an electron is given by: \[ \lambda = \frac{h}{p} \] where \( h \) is Planck's constant and \( p \) is the momentum of the electron. The momentum \( p \) can be related to the kinetic energy \( K \) of the electron: \[ K = eV = \frac{p^2}{2m} \] where \( e \) is the electron charge, \( V \) is the potential difference, and \( m \) is the mass of the electron. Step 2: Use the known values.
For \( V = 200 \, \text{kV} \), \( e = 1.6 \times 10^{-19} \, \text{C} \), and \( m = 9.11 \times 10^{-31} \, \text{kg} \), we find the best resolution to be between 2.30 and 3.20 picometers.