Question

Nuclei have energy levels just as atoms do. An excited nucleus can make a transition to a lower energy level by emitting a gamma-ray photon. The lifetime of a typical nuclear excited state is about $1 \mathrm{ps}$. What is the uncertainty in the energy of the gamma-rays emitted by a typical nuclear excited state? [Hint: Use the energytime uncertainty principle, Eq. (28-3).]

Name: Problem 25, Chapter 28: College Physics
Uploaded: 2022-01-07T17:14:43-08:00
Duration: 1 min 44 s
Channel: Manik Pulyani
Description: Nuclei have energy levels just as atoms do. An excited nucleus can make a transition to a lower energy level by emitting a gamma-ray photon. The lifetime of a typical nuclear excited state is about 1 ps. What is the uncertainty in the energy of the gamma-rays emitted by a typical nuclear excited state? [Hint: Use the energytime uncertainty principle, Eq. (28-3).]

   Nuclei have energy levels just as atoms do. An excited nucleus can make a transition to a lower energy level by emitting a gamma-ray photon. The lifetime of a typical nuclear excited state is about $1 \mathrm{ps}$. What is the uncertainty in the energy of the gamma-rays emitted by a typical nuclear excited state? [Hint: Use the energytime uncertainty principle, Eq. (28-3).]

College Physics

lan Giambattista,… 2nd Edition

Chapter 28, Problem 25

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Solved by Expert Manik Pulyani

01/07/2022

Step 1

Step 1: The energy-time uncertainty principle is given by the equation: \[ \Delta E \Delta t \geq \frac{\hbar}{2} \] where $ \Delta E $ is the uncertainty in energy, $ \Delta t $ is the uncertainty in time, and $ \hbar $ is the reduced Planck constant. Show more…

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Nuclei have energy levels just as atoms do. An excited nucleus can make a transition to a lower energy level by emitting a gamma-ray photon. The lifetime of a typical nuclear excited state is about $1 \mathrm{ps}$. What is the uncertainty in the energy of the gamma-rays emitted by a typical nuclear excited state? [Hint: Use the energytime uncertainty principle, Eq. (28-3).]

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Key Concepts

Excited State Lifetime and Energy Broadening

In quantum systems, an excited state that exists for a short duration (a brief lifetime) naturally leads to an intrinsic uncertainty or broadening in its energy level. This phenomenon manifests as a range of possible energies (or linewidth) in the emitted radiation during transitions, highlighting the probabilistic and wave-like nature of particles in quantum mechanics.

Energy-Time Uncertainty Principle

This principle in quantum mechanics states that the uncertainty in the measurement of energy (?E) and the uncertainty in the measurement of time (?t) are inversely related, with their product bounded by a constant (typically involving ?). It implies that a short lifetime of an excited state leads to a comparatively large spread in the energy levels, reflecting the fundamental limits of simultaneous precision in time and energy measurements.

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