Physics Atoms

$r_n=a_0{n}_2$

$\begin{array}{rr}& {\mathrm{r}}_1={\mathrm{a}}_0=5.3*{10}^{-11}\mathrm{m}\\ & {\mathrm{r}}_3={\mathrm{a}}_0\left(3\right)2\\ & =5.3*{10}^{-11}*9\\ & =4.77\text{?}\end{array}$

$?\frac{1}{\lambda }=\mathrm{R}\left(\frac{1}{{\mathrm{n}}_2^2}-\frac{1}{{\mathrm{n}}_1^2}\right)$

$\Rightarrow \frac{1}{\lambda }=\mathrm{R}\left(\frac{1}{2^2}\right)$

$\Rightarrow \lambda =\frac{4}{\mathrm{R}}$

$\frac{1}{{\lambda }^{\mathrm{\text{'}}}}=\mathrm{R}\left(\frac{1}{4^2}\right)$

$\Rightarrow {\lambda }^{\mathrm{\text{'}}}=\frac{16}{\mathrm{R}}$

$\Rightarrow {\lambda }^{\mathrm{\text{'}}}=4\lambda$

$\mathrm{e}\mathrm{V}=$ Energy of electron

for minimum wavelength, maximum loss of energy

$\mathrm{e}\mathrm{V}=\left(\frac{\mathrm{h}\mathrm{c}}{\lambda }\right)$

$\lambda \propto \left(\frac{1}{\mathrm{V}}\right)$

Hydrogen shows many spectral lines because of the following reasons. 

• Its electron can occupy many levels (n = 1, 2, 3.). 

• Each line in the hydrogen spectrum actually represents the transition from higher to lower energy levels. 

• These lines are grouped by the final energy level (Lyman n'=1, Balmer n'=2, etc.) 

• Higher energy levels are closer together. They tend to create more possible transitions.

Hydrogen produces a line spectrum because electrons exist only in discrete, quantised energy levels. When electrons jump between these fixed energy states, they emit photons with specific energies (E = h? ). This creates distinct spectral lines instead of continuous wavelengths. Bohr's model explains this through quantised orbits. Classical physics, on the other hand, would predict a continuous spectrum.

The hydrogen emission spectrum contains several spectral series, each named after its discoverer.

• Lyman series (n' = 1): To ground state, visible only in ultraviolet region
• Balmer series (n' = 2): Transitions to second level, appearing in visible region
• Paschen series (n' = 3): Moved to third level, visible in the infrared region
• Brackett series (n' = 4): Transitions to fourth level, appearing in the far infrared region
• Pfund series (n' = 5): Transitions to fifth level, showing in the infrared region
• Humphreys series (n' = 6): Transitions to sixth level, appearing in the infrared region

In the frame of car

$\mathrm{N}=\mathrm{m}\mathrm{g}$

and  $\mathrm{f}=\mathrm{m}\mathrm{a}$

$\mathrm{f}\le \mu \mathrm{N}$

$\Rightarrow \mathrm{a}\le \mu \mathrm{g}$

$\Rightarrow \mathrm{a}\le 1.5{\mathrm{m}\mathrm{s}}^{-2}$

${\mathrm{a}}_{\mathrm{m}\mathrm{a}\mathrm{x}}=1.5{\mathrm{m}\mathrm{s}}^{-2}$

When white light passes through a cool gas, atoms absorb specific wavelengths. This produces a continuous background with dark lines at those absorbed wavelengths. This is atomic absorption spectra. But when atoms are excited, they release photons at specific wavelengths, producing a dark background with bright lines. That is emission spectra. 

Every element has a unique set of spectral lines as its electrons occupy specific energy levels. What scientists know for certain is that these unique patterns act like fingerprints. It helps in identifying elements in stars, flames, or unknown samples. For instance, Helium was discovered in the Sun's spectrum before it was found on Earth.