Question

An electron microscope uses electrons accelerated through 50 kV. Find the de-Broglie wavelength of these electrons. If other factors like numerical aperture etc. are roughly the same, how does the resolving power of an electron microscope compare with that of an optical microscope which uses variable light?

Solution

Correct option is

The de-Broglie wave length of V-volt ‘electron’ is given by 

           

.        

  

              

The mean wavelength of visible light may be taken to be , which is 105 times the wavelength of 50-kV electrons. 

Now, the resolving power of a microscope is inversely proportional to the wavelength of the radiation used. Thus, the resolving power of electron microscope will be 105 times higher than that of optical microscope.    

SIMILAR QUESTIONS

Q1

Calculate the de-Broglie wavelength of a proton of kinetic energy 500 eV. The mass of proton is 

.

Q2

For what kinetic energy of a neutron will the associated de-Broglie wavelength be ? The mass of neutron is 

Q3

A particle is moving three times as fast as an electron. The ratio of the de-Broglie wavelength of the particle to that of the electron is . Calculate the particle’s mass and identify the particle.

Q4

An electron and a photon each has a wavelength 1.00 nm. Find their momenta. Given, 

Q5

Crystal diffraction experiments can be performed using X-rays or electron accelerated through appropriate voltage. Which probe, an X-ray photon or the electron, has greater energy? Take the wavelength of either probe equal to 1 Å, which is of the order of interatomic spacing in the crystal lattice. Mass of electron is .  

   

Q6

Obtain de-Broglie wavelength of a neutron of kinetic energy 150 eV. As we have seen in last example, an electron beam of 150 eV energy is suitable for crystal diffraction experiments. Would a neutron beam of the same energy by equally? Explain. The mass of neutron is .

Q7

X-rays of wavelength 0.82 Å fall on a metal plate. Find the smallest wavelength associated with the emitted photoelectrons. The work function of the metal is zero.  

.

Q8

Obtain the de-Broglie wavelength associated with thermal neutrons at room temperature (27o C). hence explain why a fast neutron beam needs to be thermalised with the environment before it can be used for neutron diffraction experiments. The mass of neutron is  and the Boltzmann constant . 

Q9

Calculate the de-Broglie wavelength of an electronic energy 100 eV.

Q10

The force exerted by a magnetic field on a charged particle is independent of the