How much energy is imparted to an electron so that its de-Broglie wavelength reduces from $10^{-10} \ m$ to $0.5 \times 10^{-10} \ m$? (Let $E$ be the initial energy of the electron).

The de Broglie wavelength associated with an electron accelerated through a potential difference $V$ is $\lambda_e$ and the de Broglie wavelength associated with a proton accelerated through the same potential difference is $\lambda_p$. If their corresponding masses are $m_e$ and $m_p$,respectively,then the ratio of their de Broglie wavelengths is . . . . . . .

If the kinetic energy of an electron and a proton are equal,find the ratio of their associated de Broglie wavelengths.

The wavelength of a probe is roughly a measure of the size of a structure that it can probe in some detail. The quark structure of protons and neutrons appears at the minute length-scale of $10^{-15} \;m$ or less. This structure was first probed in early $1970s$ using high energy electron beams produced by a linear accelerator at Stanford,$USA$. Guess what might have been the order of energy of these electron beams. (Rest mass energy of electron $= 0.511 \;MeV$.)

$A$ particle has a de Broglie wavelength $\lambda$. If its velocity and energy are both doubled,what will be the new de Broglie wavelength?

Explain how,according to Born's probability interpretation,a wave having a single (unique) wavelength is extended all over space.