Which of the following corresponds to the energy of a possible excited state of hydrogen (in $eV$)?

The number of photons emitted by a monochromatic (single frequency) infrared range finder of power $1 \, mW$ and wavelength of $1000 \, nm$,in $0.1 \, s$ is $x \times 10^{13}$. The value of $x$ is ..... .
(Nearest integer)
$(h=6.63 \times 10^{-34} \, J \, s, c=3.00 \times 10^{8} \, m \, s^{-1})$

In the atomic spectrum of hydrogen, the wavelengths of the spectral lines corresponding to electronic transitions $(i)$ $n=4$ to $n=2$ and $(ii)$ $n=3$ to $n=1$ are $\lambda_1$ and $\lambda_2$ $\mathring{A}$ respectively. The value of $(\lambda_1-\lambda_2)$ (in cm) is ($R_H$ = Rydberg constant)

The work function for a metal is $4 \, eV$. To emit a photo electron of zero velocity from the surface of the metal,the wavelength of incident light should be : ................ $\mathring{A}$

The energy of an electron in the first Bohr orbit of $H$ atom is $-13.6 \ eV$. The energy value of an electron in the first excited state of $Li^{2+}$ is ............... $eV$.

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.