Dual Nature Of Light Question 359
Question: A cylindrical rod of some laser material $ 5\times {{10}^{-2}}m $ long and $ {{10}^{-2}} $ m in diameter contains $ 2\times 10^{25} $ ions $ 6.6\times {{10}^{-7}}m. $ per m3. If on excitation all the ions are in the upper energy level and de-excite simultaneously emitting photons in the same direction, calculate the maximum energy contained in a pulse of radiation of wavelength $ 6.6\times {{10}^{-7}}m. $ If the pulse lasts for $ {{10}^{-7}}s $ . the average power of the laser during the pulse is
Options:
A) 532 MW
B) 352 MW
C) 235MW
D) 325 MW
Show Answer
Answer:
Correct Answer: C
Solution:
[c] Total number of ions in the rod $ N=( 2\times 10^{25} )\times [ \frac{\pi }{4}\times {{( {{10}^{-2}} )}^{2}} ]\times ( 5\times {{10}^{-2}} ) $ $ =7.85\times 10^{19} $ The energy of excitation $ E=N\times \frac{hc}{\lambda } $ $ ( 7.85\times 10^{19} )\times \frac{( 6.6\times {{10}^{-34}} )\times ( 3\times 10^{8} )}{6.6\times {{10}^{-7}}} $ $ =23.55J $ Average power P $ =\frac{E}{t}=\frac{23.55}{{{10}^{-7}}}=23.55\times 10^{7}W=235MW $
BETA
