In Bohr's model of the hydrogen atom,the ratio between the period of revolution of an electron in the orbit of $n=1$ to the period of revolution of the electron in the orbit $n=2$ is

The wavelength of the first Balmer line caused by a transition from the $n=3$ level to the $n=2$ level in hydrogen is $\lambda_1$. The wavelength of the line caused by an electronic transition from $n=5$ to $n=3$ is

State the success of the Bohr's atomic model.

The magnitude of total energy and angular momentum of an electron in the $n^{th}$ orbit of a Bohr atom is denoted by $E_{n}$ and $L_{n}$ respectively. Then

$A$ proton is fired from a very large distance towards a nucleus with charge $Q = 120e$,where $e$ is the elementary charge. It reaches a distance of closest approach of $10 \ fm$. The de Broglie wavelength of the proton at its initial position is (in $fm$). (Given: mass of proton $m_p = (5/3) \times 10^{-27} \ kg$; $h/e = 4.2 \times 10^{-15} \ J \cdot s/C$; $\frac{1}{4\pi \varepsilon_0} = 9 \times 10^9 \ N \cdot m^2/C^2$; $1 \ fm = 10^{-15} \ m$)

When a hydrogen atom emits a photon of energy $12.09 \,eV$,its orbital angular momentum changes by (where $h$ is Planck's constant)