Modern physics

Einstein's mass-energy equivalence principle states that energy and mass are directly proportional, with the constant of proportionality being the square of the speed of light. Therefore, the correct formula is E = mc^2. Option A is incorrect because E = mc is dimensionally incorrect for energy, as it lacks the necessary units of velocity squared.

The number of remaining active nuclei is given by (1/2)^n, where n is the number of half-lives. Since 30 years represents exactly three half-lives (30/10 = 3), the remaining fraction is (1/2)^3, which equals 1/8. Distractor B is incorrect because 1/4 represents the fraction remaining after only two half-lives (20 years), not three.

According to Einstein's photoelectric equation, the maximum kinetic energy of emitted electrons equals the incident photon energy minus the work function needed to escape the metal. A diagram for this topic isn't available yet — the worked example below walks the same reasoning step by step.

• !Option A is incorrect because adding the work function would violate the law of conservation of energy by creating extra energy.
• !Distractor B is incorrect because 1/4 represents the fraction remaining after only two half-lives (20 years), not three.
• !Option A is incorrect because E = mc is dimensionally incorrect for energy, as it lacks the necessary units of velocity squared.
• !Option A is incorrect because the energy associated with forming an entire atom from a nucleus and electrons involves atomic ionization energy, which operates on a much smaller scale.

Answer each from memory — you'll see instantly whether you're right and why.

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