Question

The decay energy of a short-lived nuclear excited state has an uncertainty of 2.0 eV due to its short lifetime. What is the smallest lifetime it can have?

a) 3.31 × 10^(-13) s
b) 1.32 × 10^(-13) s
c) 6.63 × 10^(-14) s
d) 2.11 × 10^(-26) s

Answer 1

The smallest lifetime a nuclear excited state with an uncertainty in decay energy of 2.0 eV can have is approximately 4.136 × 10^-15 s, according to the uncertainty principle. Therefore, the smallest lifetime the nuclear excited state can have is approximately 4.136 × 10-15 s.

Step-by-step explanation:

In quantum mechanics, the uncertainty principle states that there is a fundamental limit to the precision with which certain pairs of physical properties can be known simultaneously. One such pair is energy and time.

The uncertainty in energy, ΔE, can be related to the uncertainty in time, Δt, using the equation ΔE Δt ≥ h, where h is the reduced Planck's constant. In this case, the uncertainty in decay energy, ΔE, is given as 2.0 eV.

By rearranging the equation ΔE Δt ≥ h, we can solve for the smallest uncertainty in time, Δt. Plugging in the value for ΔE as 2.0 eV and h as 4.136 × 10-15 eV·s, we find that Δt ≥ 4.136 × 10-15 s. Therefore, the smallest lifetime the nuclear excited state can have is approximately 4.136 × 10-15 s.