Hydrogen $(H)$,Deuterium $(D)$,Helium $(He^+)$,and Lithium $(Li^{2+})$ emit radiation of wavelengths $\lambda_1, \lambda_2, \lambda_3,$ and $\lambda_4$ respectively during the transition from $n = 2$ to $n = 1$. Then:

Assertion : Bohr had to postulate that the electrons in stationary orbits around the nucleus do not radiate.
Reason : According to classical physics all moving electrons radiate.

Speed of an electron in Bohr's $7^{\text{th}}$ orbit for Hydrogen atom is $3.6 \times 10^6\,m/s$. The corresponding speed of the electron in $3^{\text{rd}}$ orbit,in $m/s$ is $........\times 10^6$.

In a hydrogen atom,the radius of the $n^{th}$ Bohr orbit is $r_n$. The graph between $\log \left( \frac{r_n}{r_1} \right)$ and $\log n$ will be:

The de-Broglie wavelength associated with an electron of a hydrogen atom in its ground state is (in $\text{ Å}$)

In a hydrogen atom,the electron and proton are bound at a distance of about $0.53 \; \mathring{A}$.
$(a)$ Estimate the potential energy of the system in $eV$,taking the zero of the potential energy at infinite separation of the electron from the proton.
$(b)$ What is the minimum work required to free the electron,given that its kinetic energy in the orbit is half the magnitude of potential energy obtained in $(a)$?
$(c)$ What are the answers to $(a)$ and $(b)$ above if the zero of potential energy is taken at $1.06 \; \mathring{A}$ separation?