v = 20m/s,m = 0.5kg,h = 6.626 × 10-34 m2 kg / sΔp =p×1×10−6As we know that,
P = m×v = 0.5×20 = 10kgm/s
Δp = 10×1×10−6Δp = 10-5
Heisenberg Uncertainty principle formula is given as,∆x∆p ∆x ∆x ∆x =0.527 x 10-29 m Q6) Prove non-existence of electrons in the nucleus?A6) One of the applications is to prove that electron cannot exist inside the nucleus. But to prove it, let us assume that electrons exist in the nucleus. As the radius of the nucleus in approximately 10-14m. If electron is to exist inside the nucleus, then uncertainty in the position of the electron is given byAccording to uncertainty principle∆x ∆p =h/2πThus ∆p=h/2π∆xOr ∆p=6.62 x10-34/2 x 3.14 x 10-14Or ∆p=1.05 x 10-20 kg m/ secIf this is p the uncertainty in the momentum of electron then the momentum of electron should be at least of this order that is p=1.05*10-20 kg m/sec.An electron having this much high momentum must have a velocity comparable to the velocity of light. Thus, its energy should be calculated by the following relativistic formulaE =
From equation En is the energy value (Eigen Value) of the particle in a well. It is clear that the energy values of the particle in well are discrete not continuous.
Spontaneous emission | Stimulated emission |
1.The spontaneous emission was postulated by Bohr | 1.The stimulated emission was postulated by Einstein |
2. Additional photons are not required in spontaneous emission | 2. Additional photons are required in stimulated emission |
3.One photon is emitted in spontaneous emission | 3.Two photons are emitted in stimulated emission |
4.The emitted radiation is poly-monochromatic | 4.The emitted radiation is monochromatic |
5. The emitted radiation is Incoherent | 5. The emitted radiation is Coherent |
6. The emitted radiation is less intense | 6. The emitted radiation is high intense |
7.The emitted radiation have less directionality | 7.The emitted radiation have high directionality |
8. Example: light from sodium or mercury lamp | 8. Example: light from laser source.
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a) B12> B21
b) B12< B21
c) B12 = B21
d) No specific relation
A26) C is the correct answer.
B21 is the coefficient for the stimulated emission while B12 is the coefficient for stimulated absorption. Both the processes are mutually reverse processes and their probabilities are equal. Therefore, B12 = B21. Q27) How laser light get amplify by population inversion ? A27) Population inversion DefinitionThe number of atoms present in the excited state or higher energy state is greater than the number of atoms present in the ground state or lower energy state is called population inversion. Population inversion as name suggests that this is inverted phenomena. In general lower energy level is more populated that means it have more number of atoms in lower energy level as compared to higher energy level. But by pumping we will obtain a state when the number of atoms present in the higher energy state is greater than the number of atoms present in lower energy state. Let us consider two level energy system of energies E1 and E2 as shown in figure. Let N1 and N2 be the populations that means number of atoms per unit volume of energy levels E1 andE2 respectively. According to Boltzmann’s distribution the population of an energy level E, at temperature T is given by Ni=N0 Where N0 is the population of the lower level or ground state and k is the Boltzmann’s constant. From the above relation, the population of energy levels E1 andE2 are N1=N0N2=N0At ordinary conditionsN1>N2 i.e., the population in the ground or lower state is always greater than the population in the excited or higher states. The stage of making, population of higher energy level is greater than the population of lower energy level is called population inversion i.e. N1< N2
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