## What are Modern Physics Formulas?

Modern physics as the name suggests is an updated physics relevant to day-to-day life. It includes the concepts of atomic theory, quantum mechanics, and relativities. It is an updated version of classical physics in the sense modern physics also deals with velocity, speed but they are in extreme high conditions comparable to speed of light which is relativity, on the other hand small distances as small as atomic radii which is quantum mechanics. This branch of Physics deals with important formulae which serve as the tools to understand several underlying processes of matters and engineering.

### What is Modern Physics Formulas?

Modern physics is a branch of the physical sciences that deals with the concepts that originated after the Newtonian era. The chapters under modern physics for NEET focus on two of the most important developments in the twentieth century, some of which are relativity and quantum mechanics.

The formulas that come in the competitive examination of NEET relating to the concepts of relativity and quantum mechanics are the aforementioned modern physics formulas.

### Chapters Under Modern Physics For NEET

The chapters that cover the modern physics topics for NEET are related to the concepts of the post-Newtonian era in the physical sciences. The modern physics chapters for NEET examinations are:

Radioactive decay of substances

Dual nature of light

Nuclear physics: Fission and Fusion

Bohr’s model of the atom and X-rays

Based on these chapters under modern physics for NEET, a list of modern physics formulas is provided below. All the formulas present here encompass the modern physics topics for NEET mentioned in the modern physics chapters for NEET.

### List of Important Modern Physics Formulas

The following is the list of modern physics formulas:

The work function:

\[W = h\upsilon _{0} =\frac{hc}{\lambda 0}\]; h is the planck’s constant.

The work function is minimum for cesium (1.9 eV)

The photo effect is directly proportional to the incident light/radiation.

Therefore, 𝜈 is constant.The maximum kinetic energies of photoelectrons ejected from metal are given by the following equation: K.Emax. = eVs; where Vs is the stopping potential (independent of the intensity of light).

Intensity arising from an electric field is given by

\[I =\frac{1}{2.\epsilon _{0.E^2.c}}\]

Momentum of a photon is given by: m𝜈 = h/λ.

The equation for photoelectric effect given by Einstein is

h𝜈 = w0 + kmax

∴ hc/λ = hc/λ0 + eVs

Change in energy due to wavelength is given by

ΔE = 12400/λ(Ao)

The formula for force due to radiation of photon is given by(no transmission):

i. When light is incident perpendicularly

- a =1, r = 0

F =\[\frac{IA}{c}\], Pressure = I/c

- r = 1, a = 0

\[F =\frac{2IA}{c}\], \[P =\frac{2I}{c}\]

- When 0 < r <1 and a + r = 1

\[F = \frac{IA}{c(1 + r)}\], \[P = \frac{I}{c(1 + r)}\]

ii. When light is incident at an angle θ with vertical

- a =1, r = 0

F = I.A.cosθ/c, P = F.cosθ/A = I.cos(2θ)/c

- r = 1, a = 0

F = 2.I.A.cos2θ/c, P = 2.I.cos2θ/c

- 0 < r < 1, a + r = 1

P = I.cos2θ/c (1 + r)

De-Broglie Wavelength is given by

λ = h/mv = h/P = h/√(2mKE)

Radius and speed of electron in hydrogen like atoms is given by

rn = n2.a0/Z; a0 = 0.529 Å

vn = Z.v0/n; v0 = 2.19 x 106 m/s

Energy in nth orbit is given by

En = E1. Z2/ n2 ; For example: E1 = -13.6 eV

Wavelength corresponding to the spectral lines is provided by the following equation:

1/λ = R[1/n12 - 1/n22]

For the Lyman series n1 = 1 n2 = 2, 3, 4……..

Balmer n1 = 2 n2 = 3, 4, 5………

Paschen n1 = 3 n2 = 4, 5, 6………

The Lyman series lies in the ultraviolet region and Paschen, Brackett, and Pfund series lie in the infrared region.

The total number of possible electronic transitions from the nth state is n(n-1)/2.

The following equations are given taking the effects of nuclear motion in consideration,

rn = (0.529 Å).n2/Z.m/μ

En = (-13.6 eV).Z2/n2.μ/m

The μ used in these equations provides reduced mass

μ = Mm/(M + m); where M is the mass of the nucleus.

The minimum wavelength for x-rays is provided by

λmin = hc/eV0 = 12400/V0(volt) Å

Moseley’s law is provided by the equation

√v = a(z - b); a and b are positive constants for a type of x-rays (independent of Z)

The average radius of the nucleus is given by

R = R0A1/3, R0 = 1.1 x 10-15 M; where A is the mass number.

The binding energy of the nucleus of mass M is given by B = (ZMP - NMN - M)C2.

The alpha decay process is best given by

AZX → A-4Z-2 Y + 42 He

The Q-value is given by

Q = [m(AZX ) - m(A-4Z-2 Y) - m(42 He)]C2

The beta minus decay is given by

AZX → AZ+1Y + β- + 𝜈-

The Q-value for the decay is given by

Q = [m(AZX) - m(AZ+1Y)]C2

Beta plus decay is given by the equation,

AZX → AZ-1 Y + β + 𝜈

For which, the Q-value is

Q = [m(AZX) - m(AZ-1Y) - 2me]C2

The emission of X-rays by the capture of atomic electron

AZX + e → AZ-1 Y + 𝜈

The Q-value is provided by

Q = [m(AZX) - m(AZ-1Y)]C2

The number of nuclei at any given instant ‘t’ in radioactive decay is given by

N = N0e-λt; where λ is the decay constant.The activity of a sample is given by: A = A0e-λt

The equation for the half-life is given by: T1/2 = 0.693/λ

The average life of a sample is given by: Tav = T1/2/0.693

When a radioactive nucleus decays by two different processes with half-lives of t1 and t2, the effective half-life of the nucleus is given by:

\[\frac{1}{t}\] = \[\frac{1}{t_{1}} + \frac{1}{t_{2}}\].

## FAQs on Modern Physics Formulas for NEET

**1. What Does Modern Physics Consist of?**

Modern physics mainly consists of topics like the Photoelectric effect, Bohr’s theory, X-rays, de-Broglie wavelength, Moseley’s law, radioactivity, and nuclear physics. Overall, widely, these topics are covered under the theory of relativity and quantum mechanics.

**2. Who is the Father of Modern Physics?**

Albert Einstein is said to be the father of modern physics. Modern physics consists of concepts that are of the post-Newtonian era and are widely credited to Albert Einstein for his revolutionary discoveries of the dual nature of light, photoelectric effect and the theory of relativity.

**3. What are the topics that modern physics deal with?**

Modern physics is that branch of physics that deals with the concepts of classical physics in extreme conditions. The extreme high conditions of velocity and speed, as high as compared to that of light on one hand and on the other hand extreme low conditions like distances as small as that in atoms. The extreme high conditions are dealt with by the theory of relativity and the extreme low conditions by quantum mechanics. Modern physics also deals with important topics which can help to understand the underlying principles and theories of interactions in the matter and several important phenomena occurring in our daily real-world life including the Photoelectric effect, X-rays, Moseley’s law, radioactivity, and nuclear physics.

**4. What lays the foundation of Modern Physics?**

The foundation of modern Physics is laid by the most important topics of physics which actually forms the core of the subject. The topics are as important to be understood as any of the classical physics for the development and progress of physics. They are the deep concept of atomic theory and the models, photoelectric effect, quantum thermodynamics, black body radiation, Franck-Hertz experiment, Rutherford’s experiment, Radioactive phenomena, wave-particle duality, solid-state physics including the concept of crystallography, Stern-Gerlach experiment, perihelion precession of mercury, gravitational lensing and many more.

**5. List some important discoveries in the field of modern physics.**

Years’ Research and works of several great scientists in the field of modern physics has enriched the stream with so many discoveries and this led to the development of this branch of physics. Some of the discoveries without which we would have still remained in dark about the structure of matter and atoms are as follows:

Discovery of X-rays an extremely penetrating type of radiation by Wilhelm Rontgen

The great theory of Max Planck which explains the electromagnetic field having quantized values which are the integer multiples of a minimum constant value.

Some references of movement with speed as high as that of light by Albert Einstein. Their measurements by different calculations.

The quantized energy levels of electrons that are scattered in the atom surrounding the nuclei were proposed by Niel Bohr.

The famous theory of wave-particle duality by Louis De Broglie.

The evolution of Quantum Mechanics on the basis of theories proposed by Werner Heisenberg and Erwin Schroedinger.

**6. How important is modern physics in the real world?**

Modern physics is that branch of physics that can give an explanation to every phenomenon going on in the real world. It can give a deep insight into all that you feel and experience in real life but never think of the reasons behind them. Understanding the concept of modern physics has led to such discoveries which not only has developed the medical system but also discovered electronic media and modern computers. The theories of gravitation and theories about matter and other fundamental forces get united with the theories of modern physics which is the greatest breakthrough in physics.

**7. Why is the study of modern physics important for students and how they can be helped in the study?**

Science can develop and progress only through modern physics. A student today can be a future scientist or engineer who is expected to make some great breakthroughs in the research of physics. The students need to clear the concept of modern physics from an early stage because this concept is a bit more difficult than the rest to understand but the whole future world physics is laid on the foundation of modern physics. If the students want to pursue higher studies in the field of physics, mathematics, engineering, or research in astronomy they need to have deep and sound knowledge in modern physics. Vedantu helps the students in every phase of their study with study materials, sample papers, practice exercises in their website and learning App. Experts in Physics are available in Vedantu to clear all sorts of doubts that arise in the minds of the students.