Wave-Particle Duality Equations

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Questions and Answers

What is the relationship between energy (E) and frequency (f) in wave-particle duality?

  • E is directly proportional to f.
  • E equals $hf$. (correct)
  • E is independent of f.
  • E is inversely proportional to f.

Which equation correctly relates the speed of light (c), wavelength ($ ext{λ}$), and frequency (f)?

  • $c = rac{E}{f}$
  • $c = rac{E}{ ext{λ}}$
  • $c = ext{λ}f$ (correct)
  • $c = E imes ext{λ}$

In the equation $E = rac{hc}{ ext{λ}}$, what does the variable $ ext{λ}$ represent?

  • Mass
  • Wavelength (correct)
  • Energy
  • Frequency

Which of the following equations can be used to express the relationship between energy and mass?

<p>$E = mc^2$ (A)</p> Signup and view all the answers

What constants are involved in the equation $E = hf$?

<p>Frequency and Planck's constant (A)</p> Signup and view all the answers

What does one electron volt (eV) represent?

<p>The energy gained by an electron when moved through an electric potential difference of one volt. (C)</p> Signup and view all the answers

How many joules is one electron volt equivalent to?

<p>$1.602 imes 10^{-19}$ J (B)</p> Signup and view all the answers

In what scenario would an electron gain an energy of one electron volt?

<p>When accelerated through a potential difference of one volt. (D)</p> Signup and view all the answers

Which of the following statements about the electron volt is incorrect?

<p>It is specific to electrons only. (C)</p> Signup and view all the answers

What is the primary application of electron volts in scientific fields?

<p>To quantify the energy levels in atomic and particle physics. (A)</p> Signup and view all the answers

What does the equivalent dose measure?

<p>The absorbed dose weighted by radiation type (C)</p> Signup and view all the answers

What is the relationship between sievert and rem?

<p>1 sievert = 100 rem (A)</p> Signup and view all the answers

In the formula $H_T = \sum_{R} D_{T,R} \cdot W_R$, what does $W_R$ represent?

<p>Weighting factor for the type of radiation (C)</p> Signup and view all the answers

Which of the following represents the typical units for measuring equivalent dose?

<p>Millirem (mrem) and microsievert ($\mu$Sv) (D)</p> Signup and view all the answers

How is one millirem related to microsieverts?

<p>1 mrem = 10 $,\mu$Sv (B)</p> Signup and view all the answers

What is the SI unit of absorbed dose?

<p>Gray (A)</p> Signup and view all the answers

How many grays are equivalent to 100 rads?

<p>1 Gy (D)</p> Signup and view all the answers

What does the absorbed dose specifically measure in relation to ionizing radiation?

<p>The amount of energy deposited per mass (B)</p> Signup and view all the answers

What is the traditional unit corresponding to the absorbed dose in grays?

<p>Rad (C)</p> Signup and view all the answers

Which of the following best describes a gray (Gy)?

<p>The amount of radiation depositing 1 joule per kg of matter (C)</p> Signup and view all the answers

What is binding energy?

<p>The energy required to separate a particle from a system of particles. (C)</p> Signup and view all the answers

How does binding energy vary with atomic number?

<p>It increases as the atomic number increases. (D)</p> Signup and view all the answers

Which statement correctly describes the relationship between binding energy and the shell structure of an atom?

<p>Binding energy can vary depending on the shell occupied by the electrons. (A)</p> Signup and view all the answers

Which of the following statements about binding energy is false?

<p>Binding energy is a measure of energy emitted when particles combine. (D)</p> Signup and view all the answers

What effect does increasing binding energy generally have on a system's stability?

<p>It increases the stability of the system. (B)</p> Signup and view all the answers

Which type of electromagnetic wave has the shortest wavelength?

<p>X- and gamma rays (C)</p> Signup and view all the answers

Which of the following energy ranges corresponds to ultraviolet waves?

<p>3-12 eV (D)</p> Signup and view all the answers

What is the frequency range for infrared waves?

<p>30-430 THz (C)</p> Signup and view all the answers

Which type of wave falls within the wavelength range of 700-400 nm?

<p>Visible light (B)</p> Signup and view all the answers

Which energy level is associated with radio waves?

<p>40-200 neV (A)</p> Signup and view all the answers

What does the inverse square law for intensity indicate about the relationship between intensity and distance?

<p>Intensity decreases as distance increases. (D)</p> Signup and view all the answers

In the equation $I₁ / I₂ = d₂²/d₁²$, what does d₁ and d₂ represent?

<p>The distances from the source at which intensities are measured. (B)</p> Signup and view all the answers

Based on the inverse square law, what can be inferred about the intensity at a distance of 4 meters compared to a distance of 2 meters?

<p>The intensity at 4 meters will be one-fourth of that at 2 meters. (C)</p> Signup and view all the answers

If the intensity of a sound wave is measured at a distance of 3 meters, how will the intensity change if the distance is increased to 9 meters?

<p>The intensity will decrease by a factor of 9. (B)</p> Signup and view all the answers

Which of the following phenomena can be explained using the inverse square law for intensity?

<p>The variation in sound level as you move further from the source. (C)</p> Signup and view all the answers

What defines isotones?

<p>They share the same neutron number. (C)</p> Signup and view all the answers

Which statement is true regarding isomers?

<p>Isomers exist in different excited states. (A)</p> Signup and view all the answers

In the case of mirror nuclei, what is true about their mass number and proton/neutron relationship?

<p>They share the same mass number, with swapped proton and neutron numbers. (C)</p> Signup and view all the answers

Which of the following correctly describes Ba-137m?

<p>It exists in an isomeric state. (D)</p> Signup and view all the answers

What distinguishes Cs-137 from its decay product Ba-137?

<p>Ba-137 has a lower mass than Cs-137. (A)</p> Signup and view all the answers

Which type of radiation can remove electrons from atoms or molecules?

<p>Gamma rays (A)</p> Signup and view all the answers

What is an example of non-ionizing radiation?

<p>Microwaves (B)</p> Signup and view all the answers

Which characteristic distinguishes ionizing radiation from non-ionizing radiation?

<p>Ionizing radiation has higher energy levels than non-ionizing radiation. (D)</p> Signup and view all the answers

Which of the following does not classify as ionizing radiation?

<p>Red light (A)</p> Signup and view all the answers

What is radiation primarily defined as?

<p>Energy traveling through space (B)</p> Signup and view all the answers

What is a characteristic feature of non-ionizing radiation?

<p>It is less energetic than ionizing radiation. (C)</p> Signup and view all the answers

Which type of radiation is commonly used in medicine?

<p>Ionizing radiation (D)</p> Signup and view all the answers

Why is it necessary to control exposure to high levels of radiation?

<p>It can cause damage to matter and living tissue (C)</p> Signup and view all the answers

Sunshine is an example of which kind of radiation?

<p>Non-ionizing radiation (A)</p> Signup and view all the answers

What are examples of sources of low doses of radiation in our environment?

<p>Air, space, and earth materials (C)</p> Signup and view all the answers

Flashcards

E=mc^2

Energy equals mass times the speed of light squared. This equation shows the equivalence of mass and energy.

E=hf

Energy of a photon equals Planck's constant times frequency.

c=λf

Speed of light equals wavelength times frequency.

E=hc/λ

Energy of a photon equals Planck's constant times the speed of light divided by wavelength.

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Planck's constant

A fundamental constant in quantum mechanics that relates the energy of a photon with its frequency.

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Wave-Particle Duality

The concept that particles can exhibit wave-like properties and waves can exhibit particle-like properties.

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Electron Volt (eV)

The amount of energy acquired by an electron when accelerated through an electric potential difference of one volt.

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Energy of an electron volt

The energy equal to the charge of a single electron multiplied by one volt.

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eV to Joules

1 electron volt (eV) is equal to $1.602 imes 10^{-19}$ Joules (J).

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Absorbed Dose

The amount of energy deposited by ionizing radiation in a material.

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Gray (Gy)

The SI unit for absorbed dose. 1 Gy = 1 Joule of energy per kilogram of matter .

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Rad

Traditional unit for absorbed dose. 100 rad = 1 Gy.

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Ionizing Radiation

Radiation that can remove electrons from atoms.

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Absorbed Dose Units

Units used to measure the energy deposited (absorbed) in a material by radiation.

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Binding Energy Definition

The energy needed to separate particles from a system or disperse all particles.

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Binding Energy Dependence

Binding energy varies with the particle's shell and the element. It generally increases with atomic number.

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Isotones

Nuclides with the same number of neutrons.

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Isomers

Nuclides with the same Z and A but different excited states.

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Mirror Nuclei

Nuclides with the same A, where one's proton number equals the other's neutron number.

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Equivalent Dose

The weighted absorbed dose, expressed in sieverts (Sv).

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Sievert (Sv)

The unit of equivalent dose.

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Radiation Weighting Factor

A factor used to account for the biological effect of different types of radiation on tissue.

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Dose to tissue T, radiation R (DT,R)

The amount of absorbed radiation in tissue T caused by radiation R.

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1 Sv = 100 rem

Conversion factor between sieverts and rem, units of dose.

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Millirem (mrem)

A smaller unit to measure equivalent dose, $10^{-3}$ rem.

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Microsievert ($\mu$Sv)

A very small unit of equivalent dose, $10^{-6}$ Sv.

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1 mrem = 10 $\mu$Sv

A conversion factor between millirem and microsievert.

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Radio wave wavelength range

Electromagnetic waves with wavelengths from 30 meters to 6 meters

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Infrared wavelength range

Electromagnetic waves with wavelengths from 10 micrometers to 0.7 micrometers

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Visible light wavelength range

Electromagnetic waves with wavelengths from 700 nanometers to 400 nanometers

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Ultraviolet wavelength range

Electromagnetic waves with wavelengths from 400 nanometers to 100 nanometers

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X-ray/gamma-ray wavelength range

Electromagnetic waves with wavelengths from 60 picometers to 2.5 picometers

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Electromagnetic waves energy

Energy of EM waves is related to their frequency.

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Ionizing Radiation

Radiation with enough energy to remove electrons from atoms or molecules.

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Non-Ionizing Radiation

Radiation that doesn't have enough energy to remove electrons.

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Examples of Ionizing Radiation

Alpha, Beta, Gamma, X-rays, and Neutrons.

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Examples of Non-Ionizing Radiation

Light, UV, infrared, microwaves, radio waves.

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Radiation and Electrons

Ionizing radiation removes electrons, non-ionizing radiation does not.

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Inverse Square Law

The intensity of a source is inversely proportional to the square of the distance from the source.

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Radiation

Energy traveling through space.

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Intensity

The strength or power of a source per unit area.

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Ionizing Radiation

Radiation that can damage matter, especially living tissue.

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Radiation Types

Different types of energy moving through space, including light, heat, and forms used in medicine.

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Distance

The separation between the source and the point you're measuring the intensity at.

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Radiation Safety

Controlling exposure to high levels of radiation due to its potential harm.

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Mathematical Relationship

Intensity is inversely proportional to the square of the distance ( I ∝ 1/r² ).

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Inverse Proportion

As one value increases, the other decreases in a specific way (like 1/x² ).

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Study Notes

Wave-Particle Duality Equations

  • Energy (E) = mass (m) x speed of light (c)²
  • Energy (E) = Planck's constant (h) x frequency (f)
  • Speed of light (c) = wavelength (λ) x frequency (f)
  • Energy (E) = Planck's constant (h) x speed of light (c) / wavelength (λ)

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