Question

9. (5 pts) Figure B shows the energy levels of a material that is to be used in a laser. Which of the following wavelengths (nm) is one of the better ones at which to produce the lasing (better in the sense that the lasing is easier to produce)? There are several lasing schemes possible here, but only one of them has the corresponding wavelength listed in the answer array. a) 479 b) 333 c) 289 d) 841 e) 1033 f) 607 g) 423 h) 56.4 i) 712 j) 937 EleV) Lifetime 6 us 5us 3 ms 4 ms 2 ms 5 us ground Fig. B

Answer 1

For any laser system to work, the pumping radiation has to excite the atoms from any lower energy state to a higher energy state and thus achieve population inversion. For more efficient lasing action, two criteria must be fulfilled : 1. The lower energy state should be with minimal lifetime. 2. The higher energy state has to have as high a lifetime as possible.

In the above given diagrams,

$\bigtriangleup E = h\nu = hc/\lambda$

Thus,

$\lambda = hc/\bigtriangleup E$

(here h = Planck's constant, which is 4.135667×10⁻¹⁵ eV⋅s, since the energy levels are given in eV)

Now $\bigtriangleup E$ can be calculated for each transition from the given diagram.

Only two transitions give the satisfactory $\lambda$ value of 289 nm. These are :

1. Transition from E = 2.2 eV to E = 6.5 eV

and

2. Transition from E = 6.5 eV to E = 10.8 eV

All the other transitions correspond to wavelengths which are not given in the listed options as acceptable answers. Hence, the answer must be : (c) 289 nm