Using 9a) the 1st three excited-energy levels in the Paschen series and (b) the

Question

Using 9a) the 1st three excited-energy levels in the Paschen series and (b) the ground state energy, design a fourlevel laser system using pure hydrogen gas as the lasing medium. Sketch the appropriate diagram and label all emission processes. Compute the energy level values such that the lasing population inversion occurs between second and third energy levels of the Paschen series. Determine the absorption wavelength and the las.ng wavelength. State the region of the EM spectrum that each wavelength occurs.

Explanation / Answer

Ans:- as per Paschem series for 1st 3 level and b is the ground level state energy. first of all what is paschen serier. Paschen series are that series of spectrum of the hydrogen atom or gas that are transitions between the successive higher states. and principal quantum number n = 3. now we design the four level laser system using pure hydrogen gas as lasing medium. me we sketch the diagram. suppose we are given the that value. as per diagram now we computing the energy level value such that the lasing population inversion occurs between 2nf & 3rd level as sown in figure

so that suppose as per diagram the four energy levelsE1, E2, E3, E4 with energy and N1, N2, N3, N4 with populations respectively. so that energy increase for each level E1 < E2 < E3 < E4.

Now this system is very clear for optical pumping from the ground energy state E1 to the optical pump energy band E4 excites the pure hydrogen gas atoms as a laser medium. so that this level of the pure hydrogen gas atoms decay by very fast no radiation transition from the level 3 ,E3. so that full life time of the laser transition from pure hydrogen gas atom energy level E3 – E2 is much long compared to that E4 –E3, As a population accumulates in level 3 lasing medium level. for hydrogen gas atoms relax and create start for the laser transitions passing though stimulated and spontaneous emissions into level 2, E2. so that at this level we are like the energy level 4 has very earlier decay to the ground state energy level for hydrogen gas atom. so we known before this faster de-excited hydrogen gas atom leads to a nearest negligible population in E2. so that is significant we are getting as the most highly populated E3 energy level so will be form a inversion population with the E2 energy level. so we are specially as long the inversion population of level 3 N3 is much greater then 0. so that the laser operation and optical amplification are take place. now only very small number of hydrogen gas atoms need to be excited for upper energy lasing level E3 to form inversion population. so we are proves that a 4 level for laser is very much efficient and practical as compare to the 3 level laser.

Rate Equations for 4 level laser System

dN4 = Wp(N1 – N4) – (43 + 42 + 41)N4

dN4 /dt= Wp(N1 – N4) – (43 + 42 + 41)N4

   = (Wp(N1 – N4) – N4 ) / T4

dN3 / dt = 43*N4 - (32 + 31)N3 = N4/T43 – N3 / T31

dN2 / dt  = 42N4 + 32N3 + 21N2 = N4 / T42+ N3/T32 – N3/T21

So as per energy Equation the optical pumping into level 3 is not relevant to the weak absorption wavelength

and lasing wavelength

State region of EM Spectrum for each wavelength occur equation

N3 = 3 / T43 *N4

N2 = 21/ T32  + (4321 *N3) / T42 T3 = N3

= N2/ N3 = 21 / T32 + 43 21 / T42 T3

Related Questions

Navigate

• Browse (All)
• Browse U
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.