Ch 42: Nuclear Physics

Knight Calc - Physics for Scientists and Engineers 5th Edition

Knight Calc5th EditionPhysics for Scientists and EngineersISBN: 9780137344796Not the one you use?Change textbook

Knight Calc 5th Edition

Ch 42: Nuclear Physics

Problem 38

Chapter 42, Problem 38

A 50 kg laboratory worker is exposed to 20 mJ of beta radiation. What is the dose equivalent in mrem?

Verified step by step guidance

Understand the problem: The dose equivalent in mrem is calculated using the formula: \( H = D \cdot Q \), where \( H \) is the dose equivalent, \( D \) is the absorbed dose in rad, and \( Q \) is the quality factor for the type of radiation. Beta radiation typically has a quality factor \( Q = 1 \).

Convert the absorbed dose from energy (mJ) to rad. First, recall that 1 rad = 0.01 J/kg. The absorbed dose \( D \) can be calculated using \( D = \frac{E}{m} \), where \( E \) is the energy absorbed (in joules) and \( m \) is the mass of the worker (in kilograms).

Convert the given energy from millijoules to joules: \( 20 \ \text{mJ} = 20 \times 10^{-3} \ \text{J} \).

Substitute the values into the formula for \( D \): \( D = \frac{20 \times 10^{-3}}{50} \). This will give the absorbed dose in gray (Gy). To convert to rad, recall that \( 1 \ \text{Gy} = 100 \ \text{rad} \).

Finally, calculate the dose equivalent \( H \) in mrem: \( H = D \cdot Q \cdot 1000 \), where the factor of 1000 converts rem to mrem. Use \( Q = 1 \) for beta radiation.

Verified video answer for a similar problem:

This video solution was recommended by our tutors as helpful for the problem above.

Was this helpful?

Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Radiation Dose

Radiation dose refers to the amount of energy deposited by ionizing radiation in a given mass of tissue. It is typically measured in grays (Gy) or rads, where 1 Gy equals 100 rads. In this context, the dose of 20 mJ (millijoules) of beta radiation needs to be converted into a dose unit that reflects the energy absorbed by the laboratory worker's body.

Dose Equivalent

Dose equivalent is a measure that accounts for the biological effect of different types of radiation on human tissue. It is expressed in sieverts (Sv) or rems, where 1 Sv equals 100 rems. The dose equivalent is calculated by multiplying the absorbed dose by a quality factor that reflects the type of radiation, allowing for a comparison of the potential biological impact of various radiation types.

Conversion to mrem

To express the dose equivalent in millirem (mrem), a common unit in radiation safety, one must convert the dose equivalent from rems. Since 1 rem equals 1000 mrem, the final calculation will involve converting the dose equivalent obtained from the absorbed dose and quality factor into mrem for practical understanding and safety assessments.

Recommended video:

Guided course

07:46

Unit Conversions

Related Practice

Textbook Question

Particle accelerators fire protons at target nuclei so that investigators can study the nuclear reactions that occur. In one experiment, the proton needs to have 20 MeV of kinetic energy as it impacts a ²⁰⁷Pb nucleus. With what initial kinetic energy (in MeV) must the proton be fired toward the lead target? Assume the nucleus stays at rest. Hint: The proton is not a point particle.

views

Textbook Question

You learned in Chapter 41 that the binding energy of the electron in a hydrogen atom is 13.6 eV. By how much does the mass decrease when a hydrogen atom is formed from a proton and an electron? Give your answer both in atomic mass units and as a percentage of the mass of the hydrogen atom.

views

Textbook Question

The doctors planning a radiation therapy treatment have determined that a 100 g tumor needs to receive 0.20 J of gamma radiation. What is the dose in grays?

views

Textbook Question

What is the total energy (in MeV) released in the beta-minus decay of ³H?

views

Textbook Question

An unstable nucleus undergoes alpha decay with the release of 5.52 MeV of energy. The combined mass of the parent and daughter nuclei is 452 u. What was the mass number of the parent nucleus?

views

Textbook Question

Use the graph of binding energy to estimate the total energy released if three ⁴He nuclei fuse together to form a ¹²C nucleus.

views