If the radius of the first Bohr orbit of a hydrogen atom is $a_0$, what will be the de Broglie wavelength of an electron in its third excited state (in $\pi a_0$)?

The wavelength associated with a particle of mass $9.109 \times 10^{-31} \ kg$ moving with a velocity of $1.20 \times 10^5 \ m/s$ is ....... meters.

The velocity of a de Broglie wave is represented by which of the following expressions?

$A$ body of mass $x$ $kg$ is moving with a velocity of $100$ $ms^{-1}$. Its de-Broglie wavelength is $6.62 \times 10^{-35}$ $m$. Hence,$x$ is ($h = 6.62 \times 10^{-34}$ $Js$). (in $kg$)

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

In the ground state of a hydrogen atom,an electron absorbs $1.5$ times the minimum energy $\left(2.18 \times 10^{-18} \ J\right)$ required to escape from the atom. The wavelength of the emitted electron (in $m$) is $\left(m_e = 9 \times 10^{-31} \ kg\right)$.