Question

The resolving power of a microscope is approximately equal to the wavelength of light used to illuminate the object. In an electron microscope, instead of light, the object is irradiated with a beam of electrons. If the resolving power of an electron microscope is 0.01 nm, find the kinetic energy of the electrons used.

Answer 1

To find the kinetic energy of electrons in an electron microscope with a resolving power of 0.01 nm, use the de Broglie wavelength formula and relate the resulting momentum to kinetic energy through the formula for kinetic energy of a particle in motion.

Step-by-step explanation:

The question asks about the kinetic energy of the electrons used in an electron microscope that has a resolving power of 0.01 nm.

To find this, we can use the de Broglie wavelength formula \( \lambda = \frac{h}{p} \), where \( \lambda \) is the wavelength, \( h \) is Planck's constant, and \( p \) is the momentum of the electron.

The momentum can also be related to the kinetic energy of the electron (\( K \)) and its mass (\( m \)) by the formula \( \frac{1}{2}mv^2 = K \), where \( v \) is the velocity of the electron. Here's how we can use these relations to find the kinetic energy:

1. First, calculate the momentum using the de Broglie formula: \( p = \frac{h}{\lambda} \).
2. Then, relate the momentum to kinetic energy: \( p = \sqrt{2mK} \).
3. Solve for \( K \) to get the kinetic energy.

It's important to know that electrons in an electron microscope behave as waves, which allows them to have a much smaller wavelength than visible light, increasing the microscope's resolving power.

Therefore, the electrons used have a very high kinetic energy compared to the energy of photons in visible light.