Principles of Physics: A Calculus-Based Text
5th Edition
ISBN: 9781133104261
Author: Raymond A. Serway, John W. Jewett
Publisher: Cengage Learning
expand_more
expand_more
format_list_bulleted
Question
Chapter 28, Problem 36P
To determine
The fractional uncertainty in the mass determination of
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
A π0 meson is an unstable particle produced in high-energy particle collisions. Its rest energy is approximately 135 MeV, and it exists for a lifetime of only 8.70 × 10-17 s before decaying into two gamma rays. Using the uncertainty principle, estimate the fractional uncertainty Δm/m in its mass determination.
A neutral pion 770 (rest energy = 135.0 MeV) produced in a high-energy particle experiment moves at a speed of 0.851c. After a very
short time, it decays into two y-ray photons. One of the y-ray photons has an energy of 126 MeV. What is the energy (in MeV) of the
second y-ray photon? Take relativistic effects into account.
Number i
Before decay
Units
E
mm
After decay
E₂
mu
Most of the particles known to physicists are unstable. For example, the lifetime of the neutral pion,π0, is about 8.4x10-17 s. Its mass is 135.0 MeV/c2. a) What is the energy width of the π0 in its ground state? b) What is the relative uncertainty ∆m/m of the pion’s mass?
Chapter 28 Solutions
Principles of Physics: A Calculus-Based Text
Ch. 28.1 - Prob. 28.1QQCh. 28.2 - Prob. 28.2QQCh. 28.2 - Prob. 28.3QQCh. 28.2 - Prob. 28.4QQCh. 28.5 - Prob. 28.5QQCh. 28.5 - Prob. 28.6QQCh. 28.6 - Prob. 28.7QQCh. 28.10 - Prob. 28.8QQCh. 28.10 - Prob. 28.9QQCh. 28.13 - Prob. 28.10QQ
Ch. 28 - Prob. 1OQCh. 28 - Prob. 2OQCh. 28 - Prob. 3OQCh. 28 - Prob. 4OQCh. 28 - Prob. 5OQCh. 28 - Prob. 6OQCh. 28 - Prob. 7OQCh. 28 - Prob. 8OQCh. 28 - Prob. 9OQCh. 28 - Prob. 10OQCh. 28 - Prob. 11OQCh. 28 - Prob. 12OQCh. 28 - Prob. 13OQCh. 28 - Prob. 14OQCh. 28 - Prob. 15OQCh. 28 - Prob. 16OQCh. 28 - Prob. 17OQCh. 28 - Prob. 18OQCh. 28 - Prob. 1CQCh. 28 - Prob. 2CQCh. 28 - Prob. 3CQCh. 28 - Prob. 4CQCh. 28 - Prob. 5CQCh. 28 - Prob. 6CQCh. 28 - Prob. 7CQCh. 28 - Prob. 8CQCh. 28 - Prob. 9CQCh. 28 - Prob. 10CQCh. 28 - Prob. 11CQCh. 28 - Prob. 12CQCh. 28 - Prob. 13CQCh. 28 - Prob. 14CQCh. 28 - Prob. 15CQCh. 28 - Prob. 16CQCh. 28 - Prob. 17CQCh. 28 - Prob. 18CQCh. 28 - Prob. 19CQCh. 28 - Prob. 20CQCh. 28 - Prob. 1PCh. 28 - Prob. 2PCh. 28 - Prob. 3PCh. 28 - Prob. 4PCh. 28 - Prob. 6PCh. 28 - Prob. 7PCh. 28 - Prob. 8PCh. 28 - Prob. 9PCh. 28 - Prob. 10PCh. 28 - Prob. 11PCh. 28 - Prob. 13PCh. 28 - Prob. 14PCh. 28 - Prob. 15PCh. 28 - Prob. 16PCh. 28 - Prob. 17PCh. 28 - Prob. 18PCh. 28 - Prob. 19PCh. 28 - Prob. 20PCh. 28 - Prob. 21PCh. 28 - Prob. 22PCh. 28 - Prob. 23PCh. 28 - Prob. 24PCh. 28 - Prob. 25PCh. 28 - Prob. 26PCh. 28 - Prob. 27PCh. 28 - Prob. 29PCh. 28 - Prob. 30PCh. 28 - Prob. 31PCh. 28 - Prob. 32PCh. 28 - Prob. 33PCh. 28 - Prob. 34PCh. 28 - Prob. 35PCh. 28 - Prob. 36PCh. 28 - Prob. 37PCh. 28 - Prob. 38PCh. 28 - Prob. 39PCh. 28 - Prob. 40PCh. 28 - Prob. 41PCh. 28 - Prob. 42PCh. 28 - Prob. 43PCh. 28 - Prob. 44PCh. 28 - Prob. 45PCh. 28 - Prob. 46PCh. 28 - Prob. 47PCh. 28 - Prob. 48PCh. 28 - Prob. 49PCh. 28 - Prob. 50PCh. 28 - Prob. 51PCh. 28 - Prob. 52PCh. 28 - Prob. 53PCh. 28 - Prob. 54PCh. 28 - Prob. 55PCh. 28 - Prob. 56PCh. 28 - Prob. 57PCh. 28 - Prob. 58PCh. 28 - Prob. 59PCh. 28 - Prob. 60PCh. 28 - Prob. 61PCh. 28 - Prob. 62PCh. 28 - Prob. 63PCh. 28 - Prob. 64PCh. 28 - Prob. 65PCh. 28 - Prob. 66PCh. 28 - Prob. 67PCh. 28 - Prob. 68PCh. 28 - Prob. 69PCh. 28 - Prob. 70PCh. 28 - Prob. 71PCh. 28 - Prob. 72PCh. 28 - Prob. 73PCh. 28 - Prob. 74P
Knowledge Booster
Similar questions
- If the rest energies of a proton and a neutron (the two constituents of nuclei) are 938.3 and 939.6 MeV, what is the difference in their mass in kilograms?arrow_forwardThe muon is unstable and has a mean lifetime of about 2.2 microseconds. A muon is an elementary particle similar to the electron. with an electric charge of -1 e, but with a much greater mass. The mass of a muon is 0.1135u, where the Atomic mass unit u = 1.66 x 10^-27 kg. It decays into an electron and two neutrinos. What is the energy released in this decay (in MeV)? Recall 1 eV = 1.6 x 10^-19 J).arrow_forward3. The lifetime of an unstable particle is governed by the exponential probabil- ity distribution. In particular, the probability that the particle lives for time t and then decays in the time interval to t+ dt is given by P(1) dt = e¬M a dr, where A is a positive decay constant. (a) Show that the probability that the particle eventually decays is equal to one. (b) Find an expression for the mean lifetime of the particle. (c) Find an expression for the probability that the particle lives for at least time T.arrow_forward
- An isotope with atomic mass of 39.953326 u decays by positron emission to a daughter nucleus with atomic mass of 39.951306 u. What is the endpoint energy of the positron spectrum? 860 kev 1.88 MeV 0 keV 1.37 MeVarrow_forwardWhat is the uncertainty in the energy released in the decay of a π0 due to its short lifetime?arrow_forwardOutside the nucleus, the neutron itself is radioactive and decays into a proton, an electron, and an antineutrino. The half-life of a neutron (mass = 1.675 × 10-27 kg) outside the nucleus is 10.4 min. On average, over what distance x would a beam of 3.14-eV neutrons travel before the number of neutrons decreased to 75.0% of its initial value? Ignore relativistic effects. X =arrow_forward
- What is the approximate uncertainty in the mass of a muon, as determined from its decay lifetime? Assume it's decay lifetime is 2.30 us. 2.548 x10-4° kgarrow_forwardThe neutral pion nº is an unstable subatomic particle with a mass of 135.0 MeV/c² and a lifetime of about 8.4 x 10-17 s. What is the uncertainty of the energy of the nº in its ground state? What is the relative uncertainty Am/m of its mass?arrow_forwardAn object with a rest mass of 18633.8 MeV/c2 is moving with a beta of 0.142. What is the relativistic kinetic energy (in MeV) of this object?arrow_forward
- Mu mesons are subatomic particles which are created when cosmic rays strike the top of the atmosphere. The travel downward at 99.5% of the speed of light. Mu meson counters were placed at the top and bottom of Mt. Washington, which is 6265 feet (1909.6 m) tall. Mu mesons are unstable particles with a half-life of 1.53 x 106 s. 3. a. How long does it take the mu mesons to go from the top to the bottom of the mountain? How many half-lives is this? 6.40x10 s, 4.18 half-lives If the counter at the top of the mountain detects 560 mu mesons per second, how many should be detected after 4 half-lives? b. ou naz 35 per second MacBook Pro escarrow_forwardA muon, or mu meson, has the same charge as an electron, but is 207 times as massive. a) Compared with electron-positron pair production, the pair production of a muon and antimuon requires a photon of what energy? E = _____ MeV b) What would be the minimum frequency for such a photon? f = _________ Hzarrow_forwarddecay in the discharging process to half of its maximum (V = Vo/2). This time is the half-life: t1= t1/2. 20.82 ms, 3.977v T1= 1.4 m/s Measure the time it takes for the voltage to decay to one-quarter (V = Vo/4 = (Vo/2)2) of its maximum. This is two half-lives: t2 = 2t1/2. Then divide this time by two to find the half-life (t1/2 = t2/2) 20.2-24.00 = 3.2 T2 = 3.2/2 = 1.6m/s Measure the time it takes for the voltage to grow to one-eighth (V = Vo/8 = (Vo/2)3) of its This is three half-lives, t3 = 3t1/2. Then divide this time by three to find the half-life, t1/2 = t3/3. 20.8 – 22.28= 1.48m/s T3= 1.48/3 = 0.49 m/s Take the average of the three measured values of the half-life. Estimate the precision of the measurement and state it as {half-life ± precision}…arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
College PhysicsPhysicsISBN:9781938168000Author:Paul Peter Urone, Roger HinrichsPublisher:OpenStax College
University Physics Volume 3PhysicsISBN:9781938168185Author:William Moebs, Jeff SannyPublisher:OpenStax
College Physics
Physics
ISBN:9781938168000
Author:Paul Peter Urone, Roger Hinrichs
Publisher:OpenStax College
University Physics Volume 3
Physics
ISBN:9781938168185
Author:William Moebs, Jeff Sanny
Publisher:OpenStax