## What are 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 = h𝜈0 = hc/λ0; h is the planck’s constant.

The work function is minimum for caesium (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 = ½.𝜖0.E2.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 = IA/c, Pressure = I/c

- r = 1, a = 0

F = 2IA/c, P = 2I/c

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

F = IA/c (1 + r), P = 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 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:

1/t = [1/t1 + 1/t2].

1. What Does Modern Physics Consist of?

Ans: 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?

Ans: 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.