Which of the following equations represents the velocity $(v)$ of the ejected electrons when a metal is struck with light of frequency $\nu$ and the threshold frequency of the metal is $\nu_0$? ($m_e =$ mass of electron and $h$ is Planck's constant).

The following figure shows the spectrum of an ideal black body at four different temperatures. The number of correct statement$(s)$ from the following is $..............$.
$A$. $T_4 > T_3 > T_2 > T_1$
$B$. The black body consists of particles performing simple harmonic motion.
$C$. The peak of the spectrum shifts to shorter wavelength as temperature increases.
$D$. $\frac{T_1}{v_1} = \frac{T_2}{v_2} = \frac{T_3}{v_3} \neq \text{constant}$
$E$. The given spectrum could be explained using quantization of energy.

The difference between the radii of $3^{rd}$ and $2^{nd}$ orbit of $H$ atom is $x \text{ pm}$. The difference between the radii of $4^{th}$ and $3^{rd}$ orbit of $Li^{2+}$ ion is $y \text{ pm}$. The ratio $y:x$ is equal to:

Neon gas is generally used in sign boards. If it emits strongly at $616 \, nm$,calculate $(a)$ the frequency of emission,$(b)$ distance traveled by this radiation in $30 \, s$,$(c)$ energy of a quantum,and $(d)$ number of quanta present if it produces $2 \, J$ of energy.

Going from $K$-shell to $N$-shell in case of $H$-atom :

If an electron moves from an excited state to the ground state in multiple steps in the hydrogen spectrum,and the number of lines in the visible region is $4$,then the number of lines in the infrared region is: