Question

the WW Relative Count Rate mler - 14.4 keV 57Fe -4-3-2-1 0 1 2 3 4 Velocity (mm/s) 100. A room temperature Mössbauer absorption spectrum for the 14.4 keV gamma-ray transition of "Fe is illustrated in the figure above. From the data, it can be deduced that the lifetime of the excited state is approximately (A) 100 ms (B) 100 us (C) 100 ns (D) 100 ps (E) 100 fs

The correct answer is C and I'm not sure how they got this, could you please explain?

Answer 1

sol Given Nin, nko 14.4 kev ho= 14.4 Keu use we Knovo know . Aho ho Ah) : 응 AE - Ah - from count rate diagram Va imam DE = 10 x 14.4 xió eu 3x8 Line widtta (DE) = 4.8 x 17 8 er Now we know from un-certainity principle Dest ħ at = 1.05 x 10 34 4.8x108x16x1019 At 0.136 xlo's lot = 13.6x108 es ] approximately at ~ loons ] or i Life time Hence, of excited state At = loons Answer & is correct option