Magnetic field at the centre of a hydrogen-like atom (atomic number $= Z$) due to the motion of an electron in the $n^{th}$ orbit is proportional to

Kinetic energy of an electron in one of the orbits of a hydrogen atom is $x$. Then, its total energy is . . . . . . .

The Hitomi satellite recently observed the Lyman alpha emission line ($n=2$ to $n=1$) of hydrogen-like iron ion (atomic number of iron is $26$) from the Perseus galaxy cluster. The wavelength of the line is closest to ............... $\mathring{A}$.

An atom of hydrogen gas is in an excited state $n_2$. It absorbs a photon of some energy and jumps to a higher energy state $n_1$. Then,it returns to the ground state after emitting six different wavelengths in the emission spectrum. Determine the values of $n_1$ and $n_2$.

The number of revolutions per second made by an electron in the first Bohr orbit of a hydrogen atom is of the order of

Consider an electron in the $n^{th}$ orbit of a hydrogen atom in the Bohr model. The circumference of the orbit can be expressed in terms of the de Broglie wavelength $\lambda$ of that electron as