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 resolution of an electron microscope depends on the de Broglie wavelength of the electrons, which is determined by their kinetic energy gained from the accelerating potential difference.

Answer 1

Step 1: Use the resolution formula.
The resolution \( d \) of an electron microscope is given by: \[ d = \frac{\lambda}{2} \] where \( \lambda \) is the de Broglie wavelength of the electrons. The de Broglie wavelength is given by: \[ \lambda = \frac{h}{p} \] where \( p \) is the momentum of the electron. The momentum \( p \) is related to the kinetic energy \( K.E. \) by: \[ K.E. = \frac{p^2}{2m} \] For electrons accelerated through a potential difference \( V \), the kinetic energy is \( K.E. = eV \), where \( e \) is the charge of the electron and \( V \) is the potential difference.
Step 2: Calculate the wavelength.
Using the energy-momentum relation, we can solve for \( \lambda \) and find the resolution. The resolution of the microscope is calculated to be approximately 0.0035 nm.
Step 3: Conclusion.
Thus, the best possible resolution is approximately 0.0035 nm.