We know that, \(\frac{1}{\lambda}=R\left(\frac{1}{n^{2}}-\frac{1}{m^{2}}\right)=\bar{v}\)
Paschen series :
Put n = 3 and m = 4,5,6....... in equation (8.18). The wave number or wavelength of spectral lines of Paschen series which lies in infra-red region (near IR) is
\(\bar{v}=\frac{1}{\lambda}=R\left(\frac{1}{3^{2}}-\frac{1}{m^{2}}\right)\)
Brackett series :
Put n = 4 and m = 5,6,7........ in equation 1. The wave number or wavelength of spectral lines of Brackett series which lies in infra-red region (middle IR) is,
\(\bar{v}=\frac{1}{\lambda}=\mathrm{R}\left(\frac{1}{4^{2}}-\frac{1}{\mathrm{~m}^{2}}\right)\).
Pfund series :
Put n = 5 and m = 6,7,8........ in equation 1. The wave number or wavelength of spectral lines of Pfund series which lies in infra-red region (far IR) is,
\(\bar{v}=\frac{1}{\lambda}=R\left(\frac{1}{5^{2}}-\frac{1}{m^{2}}\right)\).

(i) Neutrons are neutral charged (no charge).
(ii) Mass of neutron is slightly greater than proton.
(iii) Neutron is present almost all nuclei except Hydrogen 
(iv) Neutrons are stable inside the nucleus.
(v) But outside the nucleus they are unstable. If the neutron comes out of the nucleus (free neutron) it decays with emission of proton, electron and antineutrino with the half life of 13 minutes.

The circumference of an electron's orbit must be integral multiple of de Broglie wave length.
\(2 \pi r=n \lambda \)
\(\lambda=\frac{h}{m v} \)
\(2 \pi r=n \frac{h}{m v} \)
\(m v r=\frac{n h}{2 \pi} \)

(i) Gravitational force \(\mathrm{F}_{\mathrm{g}}=\mathrm{mg}=\frac{4}{3} \pi \mathrm{r}^{3} \rho \mathrm{g}\)
(ii) Electric force \(\mathrm{F}_{\mathrm{e}}=\mathrm{Eq}\)
(iii) Buoyant force \(\mathrm{F}_{\mathrm{b}}=\frac{4}{3} \pi \mathrm{r}^{3} \sigma \mathrm{g}\)
(iv) Viscous force \(\mathrm{F}_{\mathrm{v}}=6 \pi \eta \mathrm{rv}\)

(i) Pressure >110 mm of Hg - no discharge.
(ii) Pressure =100 mm of Hg - discharge - streaks of light with crackling sound.
(iii) Pressure = 10 mm of Hg - luminous column - positive column - from anode to cathode.
(iv) Pressure = 0.01 mm of Hg - crooks dark space formed - walls appear green colour- cathode rays produced.

(i) The phenomenon of spontaneous emission of highly penetrating radiations such as α, β, γ rays by heavy elements having atomic number greater than 82 is called radioactivity and the substances which emit these radiations are called radioactive elements.
(ii) The radioactive phenomenon spontaneous and is unaffected by any external agent like temperature, pressure, and magnetic fields.

(i) Fusion requires high temperature controlled reaction is not yet obtained. Highly sophisticated technology will be required.
(ii) However, the fuel is easily available, cheap and causes very less pollution.
(iii) There is no problem of waste management.
(iv) Fission controlled chain reaction is possible. The technology is well developed and established.
(v) There also exists the problem of waste management.

(i) Energy-produced per fusion is less but the number of nuclei per unit mass is larger on account of smaller mass number.
(ii) So, energy released per unit mass is greater. On the other hand, the fissionable materials have high atomic weight.
(iii) The number of fission nuclei per unit mass is less. So, energy released is less.

(i) Since proton number and neutron number are conserved in a nuclear reaction, the total rest mass of neutrons and protons is the same on either side of a reaction.
(ii) But the total binding energy of nudei on the left side need not be the same as that on the right hand side.
(iii) The difference in these binding energies appears as energy released or obsorbed in nuclear reaction.

Atomic mass unit is defined as \(\frac{1}{12}\) ^th of the mass of one \(_{ 6 }^{ 12 }{ C }\) atom.
E = mc²
= 1.66 x 10-27 x 3 X 108 x 3 x 108 J
= 1.66 x 9 x 10-11 J
= \(\frac { 1.66\times 9\times { 10 }^{ -11 } }{ 1.6\times { 10 }^{ -13 } } \) MeV = 931 MeV.

Rate of disintegration of a radioactive sample,
R = \(\frac{dN}{dt}\)
According to radioactive decay law
- \(\frac{dN}{dt}\) ∝ N
- \(\frac{dN}{dt}\) = λN or R = λN

The radius of the nth orbit 
\({ r }_{ n }=\frac { { n }^{ 2 }{ h }^{ 2 }{ \epsilon }_{ 0 } }{ \pi m{ Ze }^{ 2 } } \)
r₁ = 0.53Å
∴ The diameter of H₂ = 2 x r₁
= 0.53 x 2 = 1.06Å

The neutrino has the following properties
(i) It has zero charge
(ii) It has an antiparticle called anti-neutrino.
(iii) Recent experiments showed that the neutrino has very tiny mass
(iv) It interacts very weakly with the matter. Therefore, it is very difficult to detect In fact, in every second, trillions of neutrinos coming from the sun are passing through our body without any interaction.

(i) Moderators: The moderator is a material used to convert fast neutrons into slow neutrons. Usually the moderators are chosen in such a way that it must be very light nucleus having mass comparable to that of neutrons.
(ii) Hence, these light nuclei undergo collision with fast neutrons and the speed of the neutron is reduced.
(iii) A billiard ball striking a stationary billiard ball of equal mass would itself be stopped but the same billiard ball bounces off almost with same speed when it strikes a heavier mass.
(iv) This is the reason for using lighter nuclei as moderators.