Wavelength of $H^{+}$ ion with kinetic energy $1.65 \ eV$ is (mass of proton $= 1.6726 \times 10^{-27} \ kg$) (in $nm$)

If $v_0$ is the threshold frequency of a metal $X$,the correct relation between de Broglie wavelength $(\lambda)$ associated with the photoelectron and the frequency $(v)$ of the incident radiation is:

The atomic masses of $He$ and $Ne$ are $4$ and $20 \ amu$,respectively. The value of the de Broglie wavelength of $He$ gas at $-73^{\circ} C$ is $M$ times that of the de Broglie wavelength of $Ne$ at $727^{\circ} C$. $M$ is

The mass of an electron is $9.1 \times 10^{-31} \ kg$. If its $K.E.$ is $3.0 \times 10^{-25} \ J$,calculate its wavelength.

$A$ metal is irradiated with light of wavelength $660 \, nm$. Given that the work function of the metal is $1.0 \, eV$,the de Broglie wavelength of the ejected electron is close to

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