An electron in a hydrogen atom first jumps from the second excited state to the first excited state and then from the first excited state to the ground state. Let the ratio of wavelength,momentum,and energy of the photons in the two cases be $x, y,$ and $z$ respectively. Select the wrong answer$(s)$:

If the radius of the first orbit of a hydrogen atom is $5.29 \times 10^{-11} \, m$,the radius of the fourth orbit will be ......... $\mathring{A}$.

The radius of a hydrogen atom in the ground state is $0.53 \ Å$. After collision with an electron,it is found to have a radius of $2.12 \ Å$. The principal quantum number $n$ of the final state of the atom is:

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.

The energy level diagram for a hydrogen-like atom is shown in the figure. The radius of its first Bohr orbit is

The radius of the first orbit of a hydrogen atom is $0.5 \, \mathring{A}$ and the speed of the electron is $2.2 \times 10^6 \, m/s$. Find the magnetic induction at the proton due to the motion of the electron in $Tesla$.