Ch 44: Particle Physics and Cosmology

Young & Freedman Calc - University Physics 14th Edition

Young & Freedman Calc14th EditionUniversity PhysicsISBN: 9780321973610당신이 사용하는 게 아니라요?교과서 변경

Young & Freedman Calc 14th Edition

Ch 44: Particle Physics and Cosmology

문제 1

44장, 문제 1

A neutral pion at rest decays into two photons. Find the energy, frequency, and wavelength of each photon. In which part of the electromagnetic spectrum does each photon lie? (Use the pion mass given in terms of the electron mass in Section $44.1$ .)

검증된 단계별 안내

Step 1: Begin by understanding the decay process. A neutral pion at rest decays into two photons. Since the pion is initially at rest, its total energy is equal to its rest energy, which is given by Einstein's equation:

E_{pion} = m_{pion} c^{2}

. The energy of the pion is distributed equally between the two photons due to conservation of energy and momentum.

Step 2: Use the mass of the pion provided in Section 44.1, expressed in terms of the electron mass. The mass of the pion is approximately

m_{pion} ≈ 273 m_{electron}

. Multiply this by the electron mass (

m_{electron} ≈ 9.11 × 10

^-31 kg) and substitute into the rest energy formula to find the total energy of the pion.

Step 3: Divide the total energy of the pion equally between the two photons. Since the pion is at rest, the photons are emitted in opposite directions with equal energy. The energy of each photon is therefore:

E_{photon} = E_{pion} /2

Step 4: Relate the energy of each photon to its frequency using Planck's equation:

E_{photon} = hν

, where

h

is Planck's constant (

h ≈ 6.63 × 10

^-34 J·s) and

ν

is the frequency of the photon. Solve for

ν

using the energy calculated in Step 3.

Step 5: Calculate the wavelength of each photon using the relationship between frequency and wavelength:

λ = c / ν

, where

c

is the speed of light (

c ≈ 3.00 × 10

⁸ m/s). Finally, identify the part of the electromagnetic spectrum to which the photons belong based on their calculated wavelength.

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주요 개념

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Energy-Mass Equivalence

Energy-mass equivalence, described by Einstein's equation E=mc², states that mass can be converted into energy and vice versa. In the context of particle decay, the rest mass of the neutral pion is converted into the energy of the resulting photons. This principle is crucial for calculating the energy of the photons produced in the decay process.

Photon Properties

Photons are massless particles that carry electromagnetic radiation. Each photon has energy (E), frequency (f), and wavelength (λ) related by the equations E=hf and c=fλ, where h is Planck's constant and c is the speed of light. Understanding these relationships is essential for determining the energy, frequency, and wavelength of the photons resulting from the pion decay.

Electromagnetic Spectrum

The electromagnetic spectrum encompasses all types of electromagnetic radiation, ranging from radio waves to gamma rays. Each type of radiation is characterized by its wavelength and frequency. Identifying the part of the spectrum where the photons lie requires calculating their wavelengths and comparing them to known ranges, which helps in understanding their physical properties and applications.