What is the ratio of the radius of the second Bohr orbit to the first Bohr orbit of the $H$ atom?

The correct representation of the wavelength-intensity relationship of an ideal black body radiation at two different temperatures $T_{1}$ and $T_{2}$ (where $T_{2} > T_{1}$) is:

If the velocity of the revolving electron of $He^{+}$ in the first orbit $(n=1)$ is $v$,what is the velocity of the electron in the second orbit $(n=2)$?

If the work function of a metal is $6.63 \times 10^{-19} \ J$,the maximum wavelength of the photon required to remove a photoelectron from the metal is $.... \ nm$. (Nearest integer)
[Given : $h = 6.63 \times 10^{-34} \ J \ s$,and $c = 3 \times 10^{8} \ m \ s^{-1}$ ]

Which energy level transition among the following will have the least wavelength?

Arrange the following wavelengths $(\lambda)$ of given emission lines of $H$ atoms in increasing order:
$(a) \ n = 3 \xrightarrow{\lambda_1} n = 1$
$(b) \ n = 12 \xrightarrow{\lambda_3} n = 10$
$(c) \ n = 5 \xrightarrow{\lambda_2} n = 3$
$(d) \ n = 22 \xrightarrow{\lambda_4} n = 20$
Choose the correct option.