An electron microscope uses electrons accelerated by a voltage of `50kV`. Determine the De Broglie wavelength associated with the electrons. If other factors ( such as numerical aperture, etc.) are taken to be roughly the same, how does the resolving power of an electron microscope compare with that of an optical microscope which uses yellow light?

Explanation

To solve the problem step by step, we will first calculate the de Broglie wavelength of the electrons accelerated by a voltage of 50 kV, and then we will compare the resolving power of the electron microscope with that of an optical microscope using yellow light.

### Step 1: Calculate the Kinetic Energy of the Electron
The kinetic energy (E) of an electron accelerated through a voltage (V) can be calculated using the formula:
\[ E = e \cdot V \]
where:
- \( e = 1.6 \times 10^{-19} \) coulombs (charge of the electron)
- \( V = 50 \times 10^3 \) volts (accelerating voltage)
...