Given the ratio of kinetic energy of an electron in two orbitals is $16:9$. Calculate the ratio of the wavelength of the electron waves.

Calculate the wavelength in nanometers associated with a particle moving with a velocity of $1.0 \times 10^3 \, m s^{-1}$. (Given: mass $m = 1.67 \times 10^{-27} \, kg$ and Planck's constant $h = 6.63 \times 10^{-34} \, J s$)

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

Which one of the following explains light both as a stream of particles and as wave motion?

The velocity $v$ of a de Broglie wave is given by
$\left[ \begin{array}{c} u = \text{Frequency} \\ m = \text{mass} \\ C = \text{Velocity of light} \end{array} \right]$

The wavelength associated with the motion of an electron: