$A$ hydrogen ion $(H^+)$ and a singly ionized helium atom $(He^+)$ are accelerated from rest through the same potential difference $(V)$. The ratio of the final speeds of the hydrogen ion and the helium ion is close to:

The de-Broglie wavelength of the electron in the ground state of a hydrogen atom is

An electron in a hydrogen atom,after absorbing energy photons,can jump between energy states $n_1$ and $n_2$ $(n_2 > n_1)$. It then returns to the ground state,emitting six different wavelengths in the emission spectrum. The energy of the emitted photons can be equal to,less than,or greater than the absorbed photon energy. Determine $n_1$ and $n_2$.

In a hydrogen atom,the electron is moving around the nucleus with a velocity of $2.18 \times 10^{6} \; m/s$ in an orbit of radius $0.528 \; \mathring{A}$. The acceleration of the electron is:

When an electron in a hydrogen atom is excited from its $4^{th}$ to $5^{th}$ stationary orbit,the change in angular momentum of the electron is (Planck's constant: $h = 6.6 \times 10^{-34} \ J \cdot s$)

An electron in the $n = 1$ orbit of a hydrogen atom is bound by $13.6\, eV$. The energy required to ionize it is........$ eV$.