The energy of the first (lowest) Balmer line of the $H$ atom is $x \ J$. The energy (in $J$) of the second Balmer line of the $H$ atom is:

Following results are observed when sodium metal is irradiated with different wavelengths. Calculate $(a)$ threshold wavelength and $(b)$ Planck's constant.

$\lambda \ (nm)$	$500, 450, 400$
$v \times 10^{-5} \ (cm \ s^{-1})$	$2.55, 4.35, 5.35$

In a mixture of $H$ and $He^{+}$ gases,all $H$ atoms and $He^{+}$ ions are excited to their first excited states. Subsequently,on de-excitation in $H$ atoms,energy is transferred to the excited $He^{+}$ ion. The quantum number $n$ of the $He^{+}$ ion after the energy is transferred is:

Supposing the electron is present in the $4^{th}$ energy level of $H$ atom. When the electron returns to the ground state,the possible transitions would be:

The photoelectric behaviour of $K$,$Li$,$Mg$,and $Ag$ metals is shown in the plot below. If light of wavelength $400 \ nm$ is incident on each of these metals,which of them will emit photoelectrons?
[Planck's constant $h=6.626 \times 10^{-34} \ J \ s$; velocity of light $c=3 \times 10^8 \ m \ s^{-1}$; $1 \ eV = 1.6 \times 10^{-19} \ J$]

Describe Rutherford's atomic model.