15.4 Mass-Energy Equivalence

• A small amount of mass can be converted into a large amount of energy because it is multiplied by the square of the speed of light.


  True
• Match the variable with its description in $E =$$mc^{2}$:


  E ↔️ Energy

  m ↔️ Mass

  c ↔️ Speed of light
• Why does the squared term $c^{2}$ in $E =$$mc^{2}$ result in a large amount of energy from a small mass?


  Converts mass efficiently
• Nuclear reactions release large amounts of energy due to mass loss.


  True
• Nuclear fission converts a small amount of mass into a large amount of energy.


  True
• Match the nuclear process with its description:

  Nuclear Fission ↔️ Splitting heavy nuclei

  Nuclear Fusion ↔️ Combining light nuclei
• What does the equation $E =$$mc^{2}$ describe in modern physics?


  Mass-energy equivalence
• Match the variable in $E =$$mc^{2}$ with its description and units:


  $E$ ↔️ Energy, Joules (J)

  $m$ ↔️ Mass, Kilograms (kg)

  $c$ ↔️ Speed of light, $3.00 \times 10^{8}$ m/s
• In Einstein's equation, $c$ represents the speed of light
• Give an example of a nuclear fission reaction using uranium-235.

  {}_{92}^{235}\text{U} + {}_{0}^{1}\text{n} \rightarrow {}_{56}^{141}\text{Ba} + {}_{36}^{92}\text{Kr} + 3{}_{0}^{1}\text{n} + \text{energy}</latex>
• How much energy is released when 1 kg of mass is converted into energy?

  $9 \times 10^{16}$ Joules
• What does the variable $c$ represent in Einstein's equation?


  Speed of light
• Mass can only be converted into energy in nuclear reactions.

  False
• Nuclear fission and fusion are examples of processes where mass is converted into energy.

  True
• The speed of light in a vacuum is approximately 3.00 \times 10^{8}</latex> m/s
• The mass-energy equivalence is described by Einstein's equation $E =$$mc^{2}$.
• Order the processes of mass-energy conversion based on the magnitude of energy released:

  1️⃣ Nuclear Fusion

  2️⃣ Nuclear Fission

  3️⃣ Particle Collisions
• Einstein's equation E = mc^{2}</latex> describes the mass-energy equivalence.
• The speed of light in a vacuum is $3.00 \times 10^{8}$ m/s.


  True
• Energy can be converted into mass in high-energy particle collisions.


  True
• What happens to mass during nuclear fission?

  Decreases
• Match the process with its description and energy release:

  Nuclear Fission ↔️ Heavy nuclei split, large energy release

  Nuclear Fusion ↔️ Light nuclei combine, extremely large energy release

  Particle Creation ↔️ Kinetic energy converts to mass
• What fundamental relationship does mass-energy equivalence describe?

  Mass and energy interchangeability
• What are two examples of processes where mass is converted into energy?

  Nuclear fission and fusion
• What is the approximate value of the speed of light in a vacuum?

  $3.00 \times 10^{8}$ m/s
• What does $c$ represent in Einstein's equation $E =$$mc^{2}$?


  Speed of light
• What is mass-energy equivalence?

  Mass can become energy
• In Einstein's equation, $c$ acts as a conversion factor between mass and energy.
• Mass-energy equivalence is described by the equation $E =$$mc^{2}$.


  True
• The equation $E =$$mc^{2}$ shows that mass and energy are interchangeable and convertible, with a small amount of mass yielding a tremendous amount of energy due to the factor of c^2
• In what processes is mass converted into energy?

  Nuclear fission and fusion
• Arrange the processes of mass-energy conversion in order from least to most energy released:

  1️⃣ Nuclear Fission

  2️⃣ Nuclear Fusion
• What is an example of a nuclear fusion reaction in the sun?

  $4{}_{1}^{1}\text{H} \rightarrow {}_{2}^{4}\text{He} +$$2{}_{1}^{0}\text{e} +$$2\nu +$$\text{energy}$
• The speed of light squared is an extremely large number, allowing even tiny amounts of mass to be converted into vast amounts of energy