Modern Physics formulae for NEET

Modern physics is a branch of physics which deals with the post-Newtonian concepts in the world of physics. It is based on the two major breakthroughs of the twentieth century: Relativity and Quantum Mechanics.

1. The work function is minimum for caesium (1.9 eV)

2. Work function W = hv₀ = hc/λ₀

3. Photo effect is directly proportional to the incident radiation

4. Photoelectrons ejected from metal have kinetic energies ranging from 0 to KE_max

Here KE_max = eV_s

5. Stopping potential (V_s ) is independent of the intensity of light

6. The intensity in terms of an electric field is given by

I = ½ Є₀E²C

7. The momentum of one photon is h/λ

8. Einstein equation for the photoelectric effect

hv = w₀ + KE_max

9. De Broglie wavelength

λ = h/mv = h/p

10. Radius and speed of the electron in hydrogen-like atoms

r_n = (n²/Z )a₀

a₀ = 0.529 Å

v_n = (Z/n) v₀

v₀ = 2.19 x 10⁶ m/s

11. Energy in nth orbit

E_n = E₁.(Z²/n²)

E₁ = -13.6 eV

12. Wavelength corresponding to spectral lines

1/λ = R [1/n₁² – 1/n₂²]

For layman series n₁ = 1 n₂= 2,3,4…..

Balmer series n₁ = 2 n₂= 3,4, 5…..

Paschen n₁= 3 n₂ = 4,5,6….

The Lyman series is in ultraviolet and Paschen, Brackett, Pfund series in the infrared region

13. If the effect of nucleus motion is considered

r_n=(0.529 Å) (n²/Z) (m/μ)

En= (-13.6 eV) (Z²/n²)(μ/m)

μ is the reduced mass

14. Minimum wavelength for x-rays

λmin = hc/eV₀ = 12400/V₀ Å

15. Moseley’s Law

√v = a(z – b)

a and b are positive constants

16. Average radius of the nucleus may be written as

R = R₀A^1/3

R₀ = 1.1 x 10-15 M

A – mass number

17. Binding energy of nucleus of mass M is given by

B = (ZMp + NM_N – M)C²

18. Alpha decay process

_zX^A ➡️ _z-2 Y ^A-4 + ₂He⁴

Q value = [m(_zX^A) – m(_z-2 Y ^A-4) -m(₂He⁴)]C²

19. Beta-minus decay

_zX^A ➡️ _z+1 Y ^A + β^– + v^–

Q value = [m(_zX^A) – m(_z+1 Y ^A)]C²

Beta plus decay

_zX^A ➡️ _z-1 Y ^A + β⁺ + v

Q value = [m(_zX^A) – m(_z-1 Y ^A) – 2me)]C²

20. Electron capture

_zX^A + e ➡️ _z-1 Y ^A + v

Q value = [m(_zX^A) – m(_z-1 Y ^A)]c²

21. In radioactive decay, the number of nuclei at an instant is given by N = N₀ e^-λt

22. Activity of sample A = A₀e^-λt

23. Activity per unit mass are called specific activity

24. Half life T_1/2 = 0.693/λ

25. Average life Tav= T_1/2 /0.693

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