If $E$ and $L$ denote the magnitude of total energy and angular momentum of a revolving electron in the $n^{th}$ Bohr orbit, then:

Speed of electron in its $1^{st}$ Bohr's orbit is given by $2.18 \times 10^6 \ m/s$. If the time period of electron in $n^{th}$ orbit is measured as $4.10 \ fs$,the value of $n$ is

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?

The number of revolutions per second made by an electron in the first Bohr orbit of a hydrogen atom is ($h$ = Planck's constant, $m$ = mass of electron, $r$ = radius of the orbit).

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

$A$ 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?