Mass Energy Concepts: E Equals Delta MC Squared

1. A larger Δm means a more tightly bound nucleus (all else equal).

True

False

Concept: larger defect implies stronger binding. More binding energy corresponds to larger Δm. A bigger mass defect indicates a larger energy difference between bound and unbound states.

Explanation

Concept: larger defect implies stronger binding. More binding energy corresponds to larger Δm. A bigger mass defect indicates a larger energy difference between bound and unbound states.

2. If Δm is given in kg, the energy from e=Δmc² will be in:

Mev

Joules (j)

Newtons

Coulombs

Concept: SI units. SI units give joules. Using kg and m/s in e=mc² naturally produces energy in joules.

Explanation

Concept: SI units. SI units give joules. Using kg and m/s in e=mc² naturally produces energy in joules.

3. In SI units, c≈3.0×10^8______/s.

Concept: units for the speed of light. Speed of light in meters per second. The 'm' stands for meters, so c has units of m/s.

Explanation

Concept: units for the speed of light. Speed of light in meters per second. The 'm' stands for meters, so c has units of m/s.

Submit

4. If Δm=1.0×10^(-29) kg, estimate e using c²≈9×10^16.

9×10^(-13)j

9×10^(-12)j

9×10^(-45)j

9×10^13j

Concept: order-of-magnitude calculation. e≈10^(-29)×9×10^16=9×10^(-13)j. Multiply the mass difference by c² to estimate the energy.

Explanation

Concept: order-of-magnitude calculation. e≈10^(-29)×9×10^16=9×10^(-13)j. Multiply the mass difference by c² to estimate the energy.

5. Even extremely tiny mass differences can correspond to noticeable nuclear energies.

True

False

Concept: why nuclear energies are large. c² is very large. This large factor amplifies small mass defects into significant energies.

Explanation

Concept: why nuclear energies are large. c² is very large. This large factor amplifies small mass defects into significant energies.

6. If Δm increases, the nucleus’s actual mass (compared to sum of parts) is:

Higher

Lower

The same

Unrelated

Concept: meaning of a larger defect. Larger defect means nucleus mass is further below sum. A bigger Δm implies more binding energy and thus a larger reduction in mass.

Explanation

Concept: meaning of a larger defect. Larger defect means nucleus mass is further below sum. A bigger Δm implies more binding energy and thus a larger reduction in mass.

7. Which statements are correct?

E=Δmc²

1u c²≈931mev

Δm is measured in kelvin

If Δm doubles, e doubles

Concept: correct relationships and units. a, b, d are correct. Δm is a mass difference (not temperature), and the energy is proportional to Δm.

Explanation

Concept: correct relationships and units. a, b, d are correct. Δm is a mass difference (not temperature), and the energy is proportional to Δm.

Submit

8. You can compute binding energy in mev directly from Δm in u using 931 mev/u.

True

False

Concept: direct conversion method. Multiply Δm (in u) by 931 mev. This shortcut avoids converting to SI units and is standard in nuclear calculations.

Explanation

Concept: direct conversion method. Multiply Δm (in u) by 931 mev. This shortcut avoids converting to SI units and is standard in nuclear calculations.

9. If Δm=0.005 u, then e is about:

0.465 mev

4.66 mev

46.6 mev

466 mev

Concept: conversion practice. 0.005×931≈4.655 mev. Multiply Δm by 931 to get the energy in mev.

Explanation

Concept: conversion practice. 0.005×931≈4.655 mev. Multiply Δm by 931 to get the energy in mev.

10. Which quantity is most directly calculated from mass defect?

Neutron number

Binding energy

Electron affinity

Refractive index

Concept: what Δm gives you. Mass defect gives (binding) energy. Through e=mc², Δm directly yields the binding energy.

Explanation

Concept: what Δm gives you. Mass defect gives (binding) energy. Through e=mc², Δm directly yields the binding energy.

11. The conversion 1u c²≈931mev is an approximation used for convenience.

True

False

Concept: why the number is rounded. It’s a widely used rounded constant. The exact value is slightly different, but 931 mev is accurate enough for most classroom calculations.

Explanation

Concept: why the number is rounded. It’s a widely used rounded constant. The exact value is slightly different, but 931 mev is accurate enough for most classroom calculations.

12. Grade 11 wrap-up: the key computational skill is to:

Find electron shells

Convert a mass difference into an energy using e=Δmc²

Predict half-life directly

Compute temperature from charge

Concept: main skill focus. That’s the main mass defect use. Converting Δm into energy is how mass defect becomes a practical tool for estimating binding energy.

Explanation

Concept: main skill focus. That’s the main mass defect use. Converting Δm into energy is how mass defect becomes a practical tool for estimating binding energy.

13. The binding energy corresponding to mass defect is:

E=mc

E=Δm/c²

E=Δmc²

E=Δm

Concept: correct mass–energy relation. Mass–energy equivalence. Binding energy is found by multiplying the mass defect by c², which converts a mass difference into its energy equivalent.

Explanation

Concept: correct mass–energy relation. Mass–energy equivalence. Binding energy is found by multiplying the mass defect by c², which converts a mass difference into its energy equivalent.

14. If Δm doubles, the energy e doubles.

True

False

Concept: proportionality. e is proportional to Δm. Since c² is constant, doubling Δm doubles the computed binding energy.

Explanation

Concept: proportionality. e is proportional to Δm. Since c² is constant, doubling Δm doubles the computed binding energy.

15. If Δm=0.002 u and 1u c²≈931 mev, then e≈:

0.186 mev

1.86 mev

18.6 mev

186 mev

Concept: using the u→mev conversion. 0.002×931≈1.862 mev. Multiply Δm in u by 931 mev/u to estimate the binding energy.

Explanation

Concept: using the u→mev conversion. 0.002×931≈1.862 mev. Multiply Δm in u by 931 mev/u to estimate the binding energy.

16. A useful conversion is 1u c²≈______ mev.

Concept: standard conversion factor. Common nuclear conversion factor. This lets you convert mass defects in atomic mass units directly into energies in mev.

Explanation

Concept: standard conversion factor. Common nuclear conversion factor. This lets you convert mass defects in atomic mass units directly into energies in mev.

Submit

17. If Δm=0.010 u, the binding energy is closest to:

9.31 mev

93.1 mev

931 mev

0.931 mev

Concept: basic multiplication. 0.010×931=9.31 mev. This is a direct application of the conversion factor for mass defect to energy.

Explanation

Concept: basic multiplication. 0.010×931=9.31 mev. This is a direct application of the conversion factor for mass defect to energy.

18. Mev is a unit of energy commonly used for nuclear binding energies.

True

False

Concept: typical nuclear energy units. Nuclear energies are on mev scales. Using mev is convenient because nuclear binding energies are far larger than chemical energies.

Explanation

Concept: typical nuclear energy units. Nuclear energies are on mev scales. Using mev is convenient because nuclear binding energies are far larger than chemical energies.

19. Mass defect Δm is calculated as:

Nucleus mass − sum of nucleon masses

Sum of nucleon masses − nucleus mass

Proton mass − nucleus mass

Neutron mass − proton mass

Concept: definition as a subtraction. 'Sum of free parts' minus 'bound mass.' This captures the mass difference associated with the energy released when the nucleus forms.

Explanation

Concept: definition as a subtraction. 'Sum of free parts' minus 'bound mass.' This captures the mass difference associated with the energy released when the nucleus forms.