Modern Physics - Physics JEE Advanced

JEE Advanced Physics Chapters

1

General Physics

5

Electromagnetic Waves 

2

Mechanics

6

Optics

3

Thermal Physics

7

Modern Physics

4

Electricity and Magnestism

Sl. No

Name of the Concept

Key Points of Concept

Photoelectric effect

• The phenomenon of the photoelectric effect revolves around electron emission.

• The photoelectric effect shows that when light radiation is incident on a metallic surface, the electrons near the surface absorb the radiation energy and get liberated from the surface.

• These photo or light generated electrons are known as photoelectrons.

Relation between Potential and Photoelectric Current

• With an increase in the accelerating potential, the photoelectric current increases equally.

• The saturation current occurs when the photoelectric current reaches its maximum value.

• All photoelectrons are emitted from the emitter and reach the collection plate when the photoelectrons reach saturation.

Relation between Intensity of the Incident Light and Photoelectric Current

• Photocurrent does not occur if the frequency of the incident radiation or light is lower than the metal surface's minimum frequency. It rapidly declines until it reaches zero, which is also known as the cut-off frequency or the metal plate's stopping potential.

• The photoelectric current's cut-off frequency, or stopping potential, is essentially a physical feature of the metal plate.

• The photocurrent becomes zero or reaches the cut-off frequency only when the stopping potential is sufficient to drive back even the highest-energy photoelectric particles approaching with maximum kinetic energy.

4

Cathode rays

• Cathode rays are streams of fast-moving electrons emitted from the cathode (negative electrode) of a vacuum tube when a high voltage is applied between the cathode and the anode (positive electrode). 

• Properties of cathode rays:

• Cathode rays travel in straight lines and can cast sharp shadows.

• Cathode rays are deflected by electric and magnetic fields.

• Cathode rays have mass and energy.

• Cathode rays can produce heat, light, and X-rays.

• Cathode rays can ionize gases.

5

De Broglie hypothesis- dual nature of light

• De Broglie theory suggests that light behaves like both particles and waves. 

• According to De Broglie's hypothesis, the wavelength associated with momentum is too small, which explains why microscopic elements do not exhibit wave characteristics.

6

Rutherfor’s atomic model and its limitation

• Every atom consists of a tiny central core, called the atomic nucleus in which the entire positive charge and almost entire mass of the atom are concentrated.

• The atom as a whole is electrically neutral and electrons revolve around the nucleus in various circular orbits.

• As the electron revolves so it must lose energy continuously, it must spiral inwards and eventually fall into the nucleus. Therefore, atoms should emit a continuous spectrum but what we observe is a line spectrum. So this point isn’t explained by the Rutherford model which is the biggest limitation of this model.

7

Bohr’s model of hydrogen atom

• Bohr gives three postulates;

1. Every atom consists of a central core called nucleus which contains the positive charge and electrons revolve around it in their circular orbits.

2. Electrons can revolve only in certain discrete non radiating orbits, called stationary orbits for which total angular momentum of the revolving electron is an integral multiple of $\dfrac{h}{2\pi}$, where $h$ is the Planck’s constant.

3. The emission or absorption of energy occurs only when an electron jumps from one of its specified orbit to another. The difference in the total energy of electrons in the two permitted orbits is absorbed when the electron jumps from inner to the outer orbit.

8

Hydrogen Spectrum

• The hydrogen spectrum is the line spectrum of the hydrogen atom. It is a series of discrete wavelengths of electromagnetic radiation that is emitted or absorbed by hydrogen atoms. The hydrogen spectrum is important because it provides evidence for the quantized energy levels of the hydrogen atom.

9

Series of hydrogen spectrum

• Lyman series: This series corresponds to transitions from higher energy levels to the first energy level. The wavelengths of the Lyman series lines are in the ultraviolet region of the spectrum.

• Balmer series: This series corresponds to transitions from higher energy levels to the second energy level. The wavelengths of the Balmer series lines are in the visible region of the spectrum.

• Paschen series: This series corresponds to transitions from higher energy levels to the third energy level. The wavelengths of the Paschen series lines are in the infrared region of the spectrum.

• Brackett series: This series corresponds to transitions from higher energy levels to the fourth energy level. The wavelengths of the Brackett series lines are in the far infrared region of the spectrum.

• Pfund series: This series corresponds to transitions from higher energy levels to the fifth energy level. The wavelengths of the Pfund series lines are in the far infrared region of the spectrum.

10

Nucleus of an Atom

• The nucleus of an atom is a small, dense region at the center of the atom that contains the majority of the atom's mass and positive charge. The nucleus is composed of two types of particles: protons and neutrons. Protons have a positive charge and neutrons have no charge.

• The number of protons in the nucleus is called the atomic number, and it is what determines the identity of an element. The number of neutrons in the nucleus is called the neutron number, and it can vary for different isotopes of the same element.

• The nucleus of an atom is very small compared to the size of the atom as a whole. If the atom were expanded to the size of a football stadium, the nucleus would be about the size of a marble.

11

Composition of the Nucleus

• The nucleus of an atom is made up of protons and neutrons. Protons have a positive charge, and neutrons have no charge. The number of protons in the nucleus is called the atomic number, and it is what determines the identity of an element. The number of neutrons in the nucleus is called the neutron number, and it can vary for different isotopes of the same element.

12

Size of the Nucleus

• The nucleus of an atom is very small compared to the size of the atom as a whole. The radius of a nucleus is about 100,000 times smaller than the radius of the atom. This means that if the atom were expanded to the size of a football stadium, the nucleus would be about the size of a marble.

• The small size of the nucleus is due to the strong nuclear force, which holds the protons and neutrons together. The strong nuclear force is one of the four fundamental forces in nature, and it is much stronger than the electromagnetic force that holds electrons in orbit around the nucleus.

13  

Radioactivity

• Radioactivity is the process by virtue of which a heavy element disintegrates itself without being forced by any external agent to do so.

• According to laws of radioactive disintegration, the number of atoms disintegrating per second at any instant is directly proportional to the number of radioactive atoms actually present in the sample at that instant.

$-\dfrac{dN}{dt}\varpropto N$

• The half life of a radioactive element is the amount of time it takes for half of the atoms present in the sample to decay.

• Average life time of the element is obtained by calculating the total life time of all the atoms of the element and dividing it by the total number of atoms present initially in the sample of the element

14

Alpha, beta and Gamma decay

• Alpha decay is the phenomenon of emission of an alpha particle from a radioactive nucleus. Ex:

$U^{238}_{92}\longrightarrow Th^{234}_{90}+He^4_2$

• Beta decay  is the phenomenon of emission of an electron from a radioactive nucleus. Ex:

$Th^{234}_{90}\longrightarrow Pa^{234}_{91}+e^0_{-1}$

• Gamma decay is the phenomenon of emission of gamma ray photons from a radioactive nucleus. Ex:

$Ni^{60*}_{28}\longrightarrow Ni^{60}_{27}+E_{\gamma}$

15

Nuclear fission and fusion

• Nuclear fission is the process of splitting a heavy nucleus (usually A>230) into two or more lighter nuclei.

• Nuclear fusion is the process by which two or more lighter nuclei combine to produce a single heavy nucleus. 

Sl. No

Name of Concept

Formula

1.

De Broglie wavelength

$\lambda=\dfrac {h}{p}$

Or

$\lambda=\dfrac {h}{\sqrt {2mE}}$

2.

Photon energy

$E=h\nu=\dfrac {hc}{\lambda}$

3.

Einstein’s photoelectric equation and Work function

${E_k}=h\nu-\phi$

Where,

$\phi$- The work function

4. 

Threshold frequency

${\nu_o}=\dfrac {\phi}{h}$

5.

Momentum of photon

The energy of photon moving with momentum p is $E=p c$ 

Therefore, momentum p is given by:

$p=\dfrac {h \nu}{c}$ 

6. 

Bohr’s model of hydrogen atom

From 1st postulate of Bohr’s model of atom we can write;

$\dfrac{mv^2}{r}=\dfrac{KZe^2}{r^2}$

Here, $v$= velocity with which electron is moving and $r$= radius of the orbit.

From 2nd postulate,

$mvr=\dfrac{nh}{2\pi}$

From 3rd postulate,

$E_2-E_1=nh\nu$

The electron's frequency in Bohr's stationary orbit is,

$\nu=\dfrac{KZe^2}{nhr}$

Total energy of electron in Bohr’s stationary orbit is,

$E=-\dfrac{13.6}{n^2}eV$

7. 

Radioactivity

According to the law of radioactive decay, 

$-\dfrac{dN}{dt}\varpropto N$

$R=-\dfrac{dN}{dt}= \lambda N$

Here, $\lambda$ =disintegration                          constant.

Half life ($T_{1/2}$)of radioactive element is,

$T_{1/2}=\dfrac{0.693}{\lambda}$

Average life ($\tau$) is,

$\tau= \dfrac{1}{\lambda}$

The activity of an element is given as, 

$A=A_o e^{-\lambda t}$

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