If particles are moving with the same velocity,then the maximum de-Broglie wavelength will be for

The de Broglie wavelength of a proton and $\alpha$-particle are equal. The ratio of their velocities is ...... .

What are called matter waves? Name the devices which employ the use of these matter waves.

$A$ particle of mass $1 \, mg$ has the same wavelength as an electron moving with a velocity of $3 \times 10^6 \, m/s$. The velocity of the particle is (mass of electron $= 9.1 \times 10^{-31} \, kg$).

State the de-Broglie hypothesis.

Crystal diffraction experiments can be performed using $X-$rays,or electrons accelerated through an appropriate voltage. Which probe has greater energy? (For quantitative comparison,take the wavelength of the probe equal to $1\,\mathring{A}$,which is of the order of inter-atomic spacing in the lattice) $(m_{e}=9.11 \times 10^{-31}\,kg)$