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 a photon is $5200 \ \mathring{A}$. At what velocity will an electron have the same wavelength as this photon (in $m/s$)?

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 $h = 6.63 \times 10^{-34} \, J s$)

If the total energy of an electron in a hydrogen atom in an excited state is $-3.4 \text{ eV}$,then the de-Broglie wavelength of the electron is

The de Broglie wavelength of an electron in the $4^{th}$ Bohr orbit is (in $\pi a_{0}$)

The wavelength (in $m$) of a particle of mass $1.67 \times 10^{-27} \ kg$ moving with velocity of $3.97 \times 10^6 \ m \ s^{-1}$ is: