Physics Atoms

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.

We see a discrete emission spectrum when electrons inside excited atoms or ions in gases fall back from higher energy levels to lower ones. Every transition releases a photon of a specific wavelength. Usually the spectrum appears as sharp, bright lines. Dark gaps separate them. These lines are unique to each element.

On the other hand, a continuous emission spectrum is produced when hot solids, liquids, or dense gases emit radiation. This happens because of the collective motion of their atoms and electrons. We don't see sharp lines. Instead the spectrum shows a smooth and unbroken spread of all wavelengths. 

From the given relations:
mv²/r = |dU/dr| = 4|U? |r³ . (1)
mvr = nh / 2π . (2)
By combining equations (1) and (2), we can derive the radius r:
r = ( (nh)² / (4π√* (U? )*) )¹/³ ⇒ r ∝ n²/³

E ∝ m ⇒ E / 13.6 = 207 ⇒ E = 207 * 13.6eV = 2815.2eV

The Balmer series lies in the visible region of the electromagnetic spectrum.

Velocity of an electron in the nth orbit:

v ∝ 1/n

E_ground (H-atom) = -13.6 eV

E_carbon = E_ground (H-atom) * Z²/n²
For carbon, Z=6.

-13.6 eV = -13.6 eV * (6²/n²)

1 = 36/n²

n² = 36

n = 6

Binding energy = (50M? + 70M? – Msn)C²
= (50.3915 + 70.6069 – 119.902199)U²
= (1.0962U)C²
= 931 * 1.0962MeV

Binding energy per neucleon
= (931 x 1.0962)/120 MeV
= 8.5MeV

Sol. eVslop = hc/λ - φ

Slope of curve

tan θ = hc/e = constant
as intensity of incident radiation is increased, there will be no effect on graph

In Rutherford's model, electrostatic force provides the centripetal force:

$\frac{1}{4\mathrm{\pi E}{ }_{}}$_∈  

Kinetic Energy (K):

$K=\frac{1}{2}m{v}^2=\frac{e^2}{8\pi E_{0}r}$

Potential Energy (U):

$U=-\frac{1}{4\pi E_0}\cdot \frac{e^2}{r}$

Total Energy (E):

$E=K+U=-\frac{e^2}{8\pi E_{0}r}$

Note that, E is the Epsilon symbol.