Life time of a nucleus in the excited state is 10–12 sec. Calculate the probable uncertainty in energy andfrequency of a g-ray photon emitted by it.

To solve this problem, we will use the Heisenberg Uncertainty Principle, which states that the product of the uncertainty in energy (ΔE) and the uncertainty in time (Δt) is greater than or equal to the reduced Planck's constant (h/4π).

Given: Δt = 10^-12 s (lifetime of the nucleus in the excited state) h = 6.626 x 10^-34 Js (Planck's constant)

Step 1: Calculate the uncertainty in energy We rearrange the Heisenberg Uncertainty Principle to solve for ΔE: ΔE ≥ h / (4πΔt)

Substitute the given values: ΔE ≥ (6.626 x 10^-34 Js) / (4π x 10^-12 s) ΔE ≥ 5.27 x 10^-15 J

Step 2: Calculate the uncertainty in frequency We know that energy and frequency are related by the equation E = hf, where f is the frequency. We can rearrange this to solve for Δf (the uncertainty in frequency): Δf = ΔE / h

Substitute the given values: Δf = (5.27 x 10^-15 J) / (6.626 x 10^-34 Js) Δf ≈ 7.96 x 10^18 Hz

So, the probable uncertainty in energy is approximately 5.27 x 10^-15 J and the probable uncertainty in frequency is approximately 7.96 x 10^18 Hz.