The wavelength of a microscopic particle of mass $9.1 \times 10^{-31} \ kg$ is $182 \ nm$. Its kinetic energy in $J$ is: $(h = 6.625 \times 10^{-34} \ J \ s)$

If $a_0$ is denoted as the Bohr radius of the hydrogen atom,then what is the de-Broglie wavelength $(\lambda)$ of the electron present in the $n^{th}$ orbit of the hydrogen atom?

If the radius of the first orbit of hydrogen atom is $a_0$, then de Broglie's wavelength of electron in $3^{rd}$ orbit is (in $\pi a_0$)

The wavelength of electrons accelerated from rest through a potential difference of $40 \, kV$ is $X \times 10^{-12} \, m$. The value of $X$ is $......$. (Nearest integer)
Given:
Mass of electron $= 9.1 \times 10^{-31} \, kg$
Charge on an electron $= 1.6 \times 10^{-19} \, C$
Planck's constant $= 6.63 \times 10^{-34} \, J \cdot s$

If the kinetic energy of an electron is $18.2 \times 10^{-25} \ J$,its de Broglie wavelength in $nm$ is: (mass of electron $= 9.1 \times 10^{-31} \ kg$; $h = 6.626 \times 10^{-34} \ J \ s$)

$A$ moving particle may have significant wave motion,if