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 KEmax
Here KEmax = eVs
5. Stopping potential (Vs ) is independent of the intensity of light
6. The intensity in terms of an electric field is given by
I = � Є0E2C
7. The momentum of one photon is h/λ
8. Einstein equation for the photoelectric effect
hv = w0 + KEmax
9. De Broglie wavelength
λ = h/mv = h/p
10. Radius and speed of the electron in hydrogen-like atoms
rn = (n2/Z )a0
a0 = 0.529 �
vn = (Z/n) v0
v0 = 2.19 x 106 m/s
11. Energy in nth orbit
En = 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
rn=(0.529 �) (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 �
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 = R0A1/3
R0 = 1.1 x 10-15 M
A – mass number
17. Binding energy of nucleus of mass M is given by
B = (ZMp + NMN – M)C2
18. Alpha decay process
zXA ➡️ z-2 Y A-4 + 2He4
Q value = [m(zXA) – m(z-2 Y A-4) -m(2He4)]C2
19. Beta-minus decay
zXA ➡️ z+1 Y A + β– + v–
Q value = [m(zXA) – m(z+1 Y A)]C2
Beta plus decay
zXA ➡️ z-1 Y A + β+ + v
Q value = [m(zXA) – m(z-1 Y A) – 2me)]C2
20. Electron capture
zXA + e ➡️ z-1 Y A + v
Q value = [m(zXA) – 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 T1/2 = 0.693/λ
25. Average life Tav= T1/2 /0.693