Physics M.C.Q (1 Marks)

1. Mainly there are five series and each series is named after its discoverser as Lyman series, Balmer series, Paschen series, Bracked series and pfumd series.
2. According to the Bohr's theory, the wavelength of the rediations emitted from hydrogen atom is given by

Values for the quantum number ml​ are $ -1, 0, + 1$

Bohr showed that the electron in the hydrogen atom could only be found in certain selected $($quantized$)$ orbits, and no others.

Spins are paired means clockwise and anticlock wise rotation cancel each other, so it does not have any free electron.
$\therefore$ it is in dimagnetic in nature.

In atomic physics, hyperfine structure is the different effects leading to small shifts and splitting in the energy levels of atoms, molecules and ions. The name is a reference to the fine structure which results from the interaction between the magnetic moments associated with electron spin and the electrons' orbital angular momentum. Hyperfine structure, with energy shifts is typically orders of magnitude smaller than the fine structure, results from the interactions of the nucleus $($or nuclei, in molecules$)$ with internally generated electric and magnetic fields.

Atomic number of any element is equal no of electron.
Atomic no. $=$ no. of proton $=$ no of electron.

John Dalton $(1766 – 1844)$, an English chemist and physicist, is the man credited today with the development of atomic theory. However, a theory of atoms was actually formulated $2,500$ years before Dalton by an Indian sage and philosopher, known as Acharya Kanad.

The time by a photoeletron to come out after the photon strikes is approximately $10^{-10}$ seconds. This is a fact.

Key concept: Bohr's redius of orbit $($for Hydrogen and $H_2$-like atoms$)$: For an electron around a stationary nucleus, the electrostatics force of attraction provides the necessary centripetal force.

i.e., $\frac{1}{4\pi\in_0}\frac{(\text{Ze})\text{e}}{\text{r}^2}=\frac{\text{mv^2}}{\text{r}}\ .....(\text{i})$
Also $\text{mvr}=\frac{\text{nh}}{2\pi}\ .....(\text{ii})$
From equation $(i)$ and $(ii),$ radius of $n^{th}$ orbit
$\text{r}_\text{n}=\frac{\text{n}^2\text{h}^2}{4\pi^2\text{kZme}^2}=\frac{\text{n}^2\text{h}^2\in_0}{\pi\text{mZe}^2}=0.53\frac{\text{n}^2}{\text{Z}}\mathring{\text{A}}\ \Big(\text{k}=\frac{1}{4\pi\in_0}\Big)$
$\Rightarrow\ \text{r}_\text{n}\propto\frac{\text{n}^2}{\text{Z}}\text{ or }\text{r}_\text{n}\propto\frac{1}{\text{Z}}$
$\text{r}_\text{n}=\text{a}_0\frac{\text{n}^2}{\text{Z}},$ where $a_0 =$ the Bohr radius $= 53\ pm$
The atomic number $(Z)$ of lithium is $3.$
As $\text{r}_\text{n}=\text{a}_0\frac{\text{n}^2}{\text{Z}},$
Therefore, the radius of $Li^{++}$ ion in its ground statr, on the basis of Bohr's model, will be about $\frac{1}{3}$ times to that of Bohr radius.
Therefore, the radius of lithium ion is near $\text{r}=\frac{53}{3}\approx18\text{pm}.$

The angular momentum of the electron for the $n^{th}$ state is given by,
$\text{L}_\text{n}=\frac{\text{nh}}{2\pi}$
Angular momentum of the electron for $\text{n}=3,\ \text{L}_\text{i}=\frac{3\text{h}}{2\pi}$
Angular momentum of the electron for $\text{n}=2,\ \text{L}_\text{f}=\frac{2\text{h}}{2\pi}$
The torque is the time rate of change of the angular momentum.
Torque, $\tau=\frac{\text{L}_\text{f}-\text{L}_\text{i}}{\text{t}}$
$=\frac{\big(\frac{2\text{h}}{2\pi}\big)-\big(\frac{3\text{h}}{2\pi}\big)}{10^{-8}}$
$=\frac{-\big(\frac{\text{h}}{2\pi}\big)}{10^{-8}}$
$=\frac{-10^{-34}}{10^{-8}}$ $\Big[\because\frac{\text{h}}{2\pi}\approx10^{-34}\text{J}-\text{s}\Big]$
$=-10^{-42}\text{N}-\text{m}$
The magnitude of the torque is $10^{-42}$N-m.

The shape of orbitals i.e. number of orbitals depends on the subshell in which they are found.
The maximum possible number of orbitals i.e. the allowed orientations in space are denoted by magnetic quantum number and is given by.$ml ​= 2l + 1$
$7 = 2l + 1$
$2l = 6$
$l = 3$

According to the uncertainty principle,
$\triangle\text{E}.\triangle\text{t}>=\frac{\text{h}}{2\pi}.$
Thus the time measured will become uncertain if $\triangle\text{E}$ is measured with high certainty.

Infinitely large transition are possible $($in principle$)$ for the hydrogen atom