The approximate ratio of the speed of light in vacuum to that of an electron in the first Bohr orbit of hydrogen atom is (in $: 1$)

If the wavelength of the first line of the Balmer series is $656.1 \ nm$,then the wavelength of the second line of this series will be ............. $nm$.

The work function for a caesium atom is $1.9 \, eV$. Calculate $(a)$ the threshold wavelength and $(b)$ the threshold frequency of the radiation. If the caesium element is irradiated with a wavelength of $500 \, nm$,calculate the kinetic energy and the velocity of the ejected photoelectron.

The value of Planck's constant is $6.63 \times 10^{-34} \, J \cdot s$ and the speed of light is $3.0 \times 10^8 \, m \cdot s^{-1}$. The wavelength of a quantum of light with a frequency of $8 \times 10^{15} \, s^{-1}$ is closest to which of the following values in meters?

The energy of an electron in the first orbit of $He^+$ is $-871.6 \times 10^{-20} \ J$. The energy of an electron in the first orbit of hydrogen is ...... .

If the maximum kinetic energy of photoelectrons ejected from a metal surface when it is irradiated with a radiation of frequency $4 \times 10^{14} \ s^{-1}$ is $6.63 \times 10^{-20} \ J$,then the threshold frequency of the metal is