The de-Broglie wavelength associated with a hydrogen molecule moving with a thermal velocity of $3 \ km/s$ will be ............ $\mathring{A}$.

An electron in an electron microscope with initial velocity $v_{0} \hat{i}$ enters a region of a stray transverse electric field $E_{0} \hat{j}$. The time taken for the change in its de-Broglie wavelength from the initial value of $\lambda$ to $\lambda / 3$ is proportional to

De Broglie waves are associated with moving particles. These particles can be .......

An electron,an $\alpha$-particle,and a proton have the same kinetic energy. Which of these particles has the shortest de Broglie wavelength?

$A$ particle is moving along the $x-$axis back and forth in a box of length $L$. Assuming the de-Broglie hypothesis is applicable for the particle,and it is moving with a constant speed in the box making perfectly elastic collisions with the walls. The possible value of the momentum of the particle is (Note: $h$ is Planck's constant,$n$ is the principal quantum number).

What is the ratio of the de Broglie wavelengths of a proton and a neutron moving with the same velocity?