The additional energy that should be given to an electron to reduce its de-Broglie wavelength from $1 \ nm$ to $0.5 \ nm$ is

When the momentum of a proton is changed by an amount $p_0$,the corresponding change in the de-Broglie wavelength is found to be $0.25\%$. Then,the original momentum of the proton was

The de-Broglie wavelength of an electron having $80 \ eV$ of energy is nearly .............. $\mathring{A}$ ($1 \ eV = 1.6 \times 10^{-19} \ J$,Mass of electron $= 9 \times 10^{-31} \ kg$,Planck's constant $= 6.6 \times 10^{-34} \ J \cdot s$).

Two points $A$ and $B$ have potentials of $20 \ V$ and $40 \ V$ respectively. An electron is accelerated from rest between them. Find the de Broglie wavelength associated with the electron at point $B$.

$(a)$ For what kinetic energy of a neutron will the associated de Broglie wavelength be $1.40 \times 10^{-10} \; m ?$
$(b)$ Also find the de Broglie wavelength of a neutron,in thermal equilibrium with matter,having an average kinetic energy of $\frac{3}{2} k T$ at $300 \; K$.

What is the de Broglie wavelength of an electron accelerated through a potential difference of $ 100 \ V $ (in $\text{Å}$)?