Matter Waves

The ratio between the de Broglie wavelengths associated with protons accelerated through a potential difference of $512 \mathrm{volts}$ and that of alpha particles accelerated through a potential difference of $\mathrm{X}$ volts is found to be one. Find the value of $\mathrm{X}$.

An electron is accelerated through a potential difference of $81 \mathrm{V}$. What is the de Broglie wavelength associated with it? To which part of electromagnetic spectrum does this wavelength correspond?

A deuteron and an alpha particle are accelerated with the same potential. Which one of the two has $\left(\mathrm{i}\right)$ greater value of de Broglie wavelength associated with it and $\left(\mathrm{ii}\right)$ less kinetic energy? Explain.

Calculate the de Broglie wavelength of a proton whose kinetic energy is equal to $81.9\times {10}^{-15} \mathrm{J}$. (Given: mass of proton is $1836$ times that of electron).

Describe briefly Davisson-Germer experiment which demonstrated the wave nature of electrons.

Briefly explain the principle and working of electron microscope.

Derive an expression for de Broglie wavelength of electrons.

An electron and an alpha particle have same kinetic energy. How are the de Broglie wavelengths associated with them related?

Write the relationship of de Broglie wavelength $\mathrm{\lambda }$ associated with a particle of mass $\mathrm{m}$ in terms of its kinetic energy $\mathrm{K}$.

A proton and an electron have same kinetic energy. Which one has greater de Broglie wavelength. Justify.

Why we do not see the wave properties of a baseball?

State de Broglie hypothesis.

Write the expression for the de Broglie wavelength associated with a charged particle of charge $\mathrm{q}$ and mass $\mathrm{m}$, when it is accelerated through a potential $\mathrm{V}$.

In an electron microscope, the electrons are accelerated by a voltage of $14 \mathrm{kV}$. If the voltage is changed to $224 \mathrm{kV}$, then the de Broglie wavelength associated with the electrons would:

The wavelength ${\lambda }_e$ of an electron and ${\mathrm{\lambda }}_{\mathrm{p}}$ of a photon of same energy $\mathrm{E}$ are related by: