Because the factor h on the right side of the Heisenberg uncertainty principle has units of Joule-seconds, it suggests that the energy of a system also has uncertainty.The uncertainty in energy depends on the length of the time interval during which a system exists.$\Delta$E$\Delta$t $\ge$h/4 $\pi$.Suppose an unstable mass is produced during a high-energy collision such that the uncertainty in its mass is me/100.(me = 9.11*10-31 kg.) How long will this particle exist?
A)6.4 * 10-20 s
B)2.3 * 10-23 s
C)1.0 * 1015 s
D)1.2 *1013 s
E)8.1 * 10-19 s

Question

Quizplus · Accepted Answer

The uncertainty in energy is given by $\Delta$E$\Delta$t $\ge$h/4 $\pi$. The uncertainty in mass is given by $\Delta$m = me/100. The energy of the particle is given by E = mc^2. Therefore, the uncertainty in energy is $\Delta$E = c^2 $\Delta$m = (3 * 10^8 m/s)^2 * (9.11 * 10^-31 kg / 100) = 8.19 * 10^-14 J. Substituting this into the uncertainty principle, we get $\Delta$t $\ge$h/4 $\pi\(\Delta$E) = (6.63 * 10^-34 J s) / (4 $\pi$ * 8.19 * 10^-14 J) = 6.4 * 10^-20 s.

Because the Factor H on the Right Side of the Heisenberg