Find the ratio of the area of the orbit of the first excited state to the ground state in a hydrogen atom.

$A$ sample of hydrogen atoms in its ground state is radiated with photons of $10.2 eV$ energy. The radiation emitted from the sample is absorbed by excited ionized $He^{+}$ ions. Which of the following statement$(s)$ is/are true?

For which one of the following,is the Bohr model not valid?

The magnetic moment of an orbital electron in the first orbit of an $\text{H}$-atom is $\mu_{B}$. What is the magnetic moment of that electron in the second orbit?

The de-Broglie wavelength of the electron in the ground state of the hydrogen atom is ..... (radius of the first orbit of hydrogen atom $= 0.53 \ \text{Å}$). (in $\text{Å}$)

In a hydrogen-like atom with atomic number $Z$,an electron is in an excited state with principal quantum number $2n$. The maximum energy of a photon that can be emitted from this state is $204 \ eV$. If the electron transitions from the $2n$ orbit to the $n$ orbit,a photon with energy $40.8 \ eV$ is emitted. The value of $n$ is: