Electron used in an electron microscope are accelerated by a voltage of 25 kV. If the voltage is increased to 100 kV then the de-Broglie wavelength associated with the electrons would

  • Option 1)

    increase by 2 times

  • Option 2)

    decrease by 2 times

  • Option 3)

    increase by 4 times

  • Option 4)

    increase by 4 times

 

Answers (1)
S subam

As we discussed in concept

De - Broglie wavelength with charged particle -

lambda = frac{h}{sqrt{2mE}}= frac{h}{sqrt{2mE}}

lambda = frac{h}{sqrt{2mqv}}
 

- wherein

E
ightarrow kinetic: energy: o! f particle

q
ightarrow charged : particle

 

 \lambda\:=\: \frac{h}{\sqrt{2mev}}\:=>\: \lambda\propto \frac{1}{\sqrt{V}}

\therefore \frac{\lambda_{2}}{\lambda_{1}}\:=\: \sqrt{\frac{V_{1}}{V_{2}}}\:=\:\sqrt{\frac{1}{4}}\:=\:\frac{1}{2}

\therefore wavelength decreases by a factor of 2.

 


Option 1)

increase by 2 times

This option incorrect.

Option 2)

decrease by 2 times

This option correct.

Option 3)

increase by 4 times

This option incorrect.

Option 4)

increase by 4 times

This option incorrect.

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