Calculate the energy in joule corresponding to light of wavelength $45 \ nm$. (Planck's constant,$h = 6.63 \times 10^{-34} \ J \ s$,speed of light,$c = 3 \times 10^8 \ m \ s^{-1}$)

When electromagnetic radiation of wavelength $310 \ nm$ falls on the surface of a metal having work function $3.55 \ eV$, the velocity of photoelectrons emitted is $x \times 10^5 \ ms^{-1}$. The value of $x$ is (Nearest integer). Given: $m_{e} = 9 \times 10^{-31} \ kg$, $h = 6.63 \times 10^{-34} \ J \cdot s$, $c = 3 \times 10^8 \ m/s$, $1 \ eV = 1.6 \times 10^{-19} \ J$.

The radius of the first Bohr orbit for hydrogen is $0.53 \ \mathring{A}$. The radius of the third Bohr orbit would be .............. $\mathring{A}$.

The wave numbers of three spectral lines of $H$ atom are considered. Identify the set of spectral lines belonging to the Balmer series. ($R =$ Rydberg constant)

The maximum energy is possessed by an electron when it is present:

An electron in an atom jumps in such a way that its kinetic energy changes from $x$ to $\frac{x}{4}$. The change in potential energy will be