$C_{60}$ emerging from a source at a speed $(v)$ has a de Broglie wavelength of $11.0 \ \mathring{A}$. The value of $v$ (in $m \ s^{-1}$) is closest to
[Planck's constant $h = 6.626 \times 10^{-34} \ J \ s$]

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 wavelength $\lambda$ of an electron in the $2^{nd}$ Bohr orbit is:

If the kinetic energy of a particle is reduced to half,the de-Broglie wavelength becomes

Two particles $A$ and $B$ are in motion. If the wavelength associated with particle $A$ is $5 \times 10^{-8} \ m$,calculate the wavelength (in $\mathring{A}$) associated with particle $B$ if its momentum is half of $A$.

The basis of the quantum mechanical model of an atom is: