Question

To what speed must an electron be accelerated from rest for it to have a de broglie wavelength of 100pm? what accelerating potential difference is needed?

Answer 1

To express of an electron we have to figure out the relationship between momentum and wavelength:

λ= $\frac{h}{p}$  =$\frac{h}{mv}$

So, velocity of an electron will be:

v= me/λ$e$h

​h= Planck's constant

$m_{e}$ = mass of the electron

Now we will see what is its value:

V= h/mcλ

$\frac{6.626 .10^{-34}J.s}{(9.109.10^{-31}kg).(100.10^{-12m)} }\\ 7.27.10^{6} m.s^{-1}$

​Now, to express accelerating potential energy difference we will use kinetic energy and charge of electron

Kinetic energy: $E_{K} =e_{E}$

But kinetic energy in terms of velocity is

:$\frac{(9.109.10^{-31}kg).(7.27.10^{6}ms^{-1})^{2} }{2.(1.602.10^{-19} C)} \\=150.210^{-31} .10^{-31} .10^{12}.10^{19}V \\ = 1.502.10^{2}V$

​What is kinetic energy?

• Kinetic energy is a type of power that a moving object or particle possesses. An item accumulates kinetic energy when work, which involves the transfer of energy, is done on it by exerting a net force.
• A moving object or particle has kinetic energy, which relies on both its mass and its rate of motion.
• we can calculate kinetic energy by first determining the work done W by a force, F, in a straightforward example.
• Consider a force parallel to a surface pushing a box of mass mm across a distance D along that surface.

​To know more about kinetic energy visit:

brainly.com/question/12669551

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