If travelling at equal speeds,the longest wavelength of the following matter waves is that for a :

The mass of a particle is $1 \, mg$ and its velocity is $4.5 \times 10^5 \, cm/s$. What will be the wavelength of this particle? $(h = 6.652 \times 10^{-27} \, erg \cdot s)$.

$A$ proton and a $Li^{3+}$ nucleus are accelerated by the same potential. If $\lambda_{Li}$ and $\lambda_{P}$ denote the de Broglie wavelengths of $Li^{3+}$ and proton respectively,then the value of $\frac{\lambda_{Li}}{\lambda_{P}}$ is $x \times 10^{-1}$. The value of $x$ is ............
(Rounded off to the nearest integer)
(Mass of $Li^{3+} = 8.3 \times \text{mass of proton}$)

What accelerating potential must be imparted to a proton beam to give it an effective wavelength of $\lambda = 0.05 \ \mathring{A}$? (Given: $m_p = 1.672 \times 10^{-27} \ kg$,$h = 6.626 \times 10^{-34} \ J \cdot s$,$e = 1.602 \times 10^{-19} \ C$)

The de-Broglie's wavelength of an electron present in the first Bohr orbit of an $H$ atom is:

The relationship between the momentum $(P)$ and the wavelength $(\lambda)$ of a particle is given by: