The wavelength of the matter wave is independent of

The kinetic energies of an electron,$\alpha$-particle,and a proton are given as $4K, 2K$,and $K$ respectively. The de-Broglie wavelengths associated with the electron $(\lambda_e)$,$\alpha$-particle $(\lambda_\alpha)$,and the proton $(\lambda_p)$ are related as follows:

$A$ light of wavelength $\lambda$ is incident on a photosensitive surface of negligible work function. The photoelectrons emitted from the surface have de-Broglie wavelength $\lambda_1$. Then the ratio $\lambda : \lambda_1^2$ is ($h =$ Planck's constant,$c =$ velocity of light,$m =$ mass of electron).

$A$ particle of mass $9.1 \times 10^{-31} \, \text{kg}$ travels in a medium with a speed of $10^{6} \, \text{m/s}$ and a photon of radiation with linear momentum $10^{-27} \, \text{kg} \cdot \text{m/s}$ travels in vacuum. The wavelength of the photon is $....$ times the wavelength of the particle.

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

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