An atom in an excited state has a lifetime of 1.2x10^-8sec; in a second excited
ID: 2172194 • Letter: A
Question
An atom in an excited state has a lifetime of 1.2x10^-8sec; in a second excited state the lifetime is 2.3x10^-8sec. What is the uncertainty in energy for the photon emitted when an electron makesa transition between these two levels.Explanation / Answer
The Heisenberg Uncertainty Principle states that the uncertainties in energy and over durations of time are related by the equation ?E*?t >= h/2p So the minimum uncertainty in energy over an interval of time of 1.1 × 10-8 s would be given by ?E(1.1 × 10-8 s) = h/2p Solving for ?E, we have ?E = 6.626 × 10-34 J · s/2p × (1.1*10-8) = 9.58 × 10-27 J So the uncertainty in energy over that time interval is ?E = 9.58 × 10-27 J