The muon has the same charge as an electron but a mass that is $207$ times greater. The negatively charged muon can bind to a proton to form a new type of hydrogen atom. How does the binding energy $E_{B\mu}$ of the muon in the ground state of a muonic hydrogen atom compare with the binding energy $E_{Be}$ of an electron in the ground state of a conventional hydrogen atom?

Suppose an electron is attracted towards the origin by a force $F = \frac{k}{r}$,where $k$ is a constant and $r$ is the distance of the electron from the origin. By applying the Bohr model to this system,the radius of the $n^{th}$ orbital of the electron is found to be $r_n$ and the kinetic energy of the electron is $K_n$. Then which of the following is true?

Monochromatic radiation is incident on a hydrogen $(H)$ sample which is in the ground state. If the hydrogen atoms emit radiation of $10$ different wavelengths after absorbing the incident radiation, then the wavelength of the incident radiation is (Let $hc = 1242 \text{ eV-nm}$) (in $\text{ nm}$)

Neglecting the reduced mass effect,which optical transition in the $He^+$ spectrum has the same wavelength as the first Lyman transition of hydrogen ($n = 2$ to $n = 1$)?

In Bohr's model of the hydrogen atom,let $PE$ represent potential energy and $TE$ represent total energy. When an electron transitions to a higher energy level,

Given below are two statements:
Statement $I$: In a hydrogen atom,the frequency of radiation emitted when an electron jumps from a lower energy orbit $(E_1)$ to a higher energy orbit $(E_2)$ is given as $hf = E_1 - E_2$.
Statement $II$: The jumping of an electron from a higher energy orbit $(E_2)$ to a lower energy orbit $(E_1)$ is associated with the frequency of radiation given as $f = (E_2 - E_1) / h$.
This condition is Bohr's frequency condition. In the light of the above statements,choose the correct answer from the options given below.