Section 7.6: Problem-Solving Strategies
Solving problems in quantum, atomic, and nuclear physics often requires a systematic approach:
- Step 1: Identify known quantities and what is to be found.
- Step 2: Choose the relevant principle or equation (e.g., E = hf, ΔE, half-life formula, E = mc²).
- Step 3: Convert all units to SI units.
- Step 4: Substitute values carefully and solve algebraically before numerical calculation.
- Step 5: Check units and magnitude for reasonableness.
Example: Half-Life Problem
A sample has a half-life of 4 hours. Find the fraction remaining after 10 hours.
Use \( N = N_0 (1/2)^{t/T_{1/2}} \)
\( N/N_0 = (1/2)^{10/4} = (1/2)^{2.5} \approx 0.177 \)
Practice Problems
- Calculate photon energy for light of wavelength 400 nm.
- Find the decay constant of a nuclide with half-life 8 hours.
- Determine energy released from converting 2 g of matter to energy.
- Calculate the wavelength of an electron with momentum 3 × 10⁻²⁴ kg·m/s.
- Sketch energy levels for hydrogen and label transitions corresponding to Balmer series.