DZI Physics and Astronomy common mistakes
DZI Physics and Astronomy · Understand the traps and how to avoid them.
When computing gravitational or electrostatic potential energy, plugging a distance into U = -GMm/r (or kQq/r) without first converting every quantity to SI base units, so a separation given in km, AU, or solar radii is used directly as r.
Astrophysics and gravitation problems habitually quote distances and masses in astronomical units, solar masses, or kilometres, and candidates carry those numbers straight into formulas whose constants (G, k) are defined in SI, producing energies wrong by factors of 10^3 to 10^11.
What to do instead
Before substituting, write a one-line unit ledger listing each variable with its value and its SI conversion (1 AU = 1.496e11 m, 1 Msun = 1.989e30 kg, 1 km = 1e3 m), then substitute only the converted values; sanity-check the answer's order of magnitude against a known binding energy such as Earth's orbital energy.
Treating a thermodynamic process as isothermal or adiabatic by assumption rather than by reading the stated constraints, then applying the wrong relation (PV = constant versus PV^gamma = constant) and getting a work or heat value that violates the first law.
Textbook problems present many superficially similar gas expansions, and candidates pattern-match on keywords like 'slow' or 'insulated' instead of checking whether heat exchange is actually permitted; the adiabatic exponent also gets confused with the ratio of specific heats written upside down.
What to do instead
For every process problem, first write down which of Q, W, and delta-U are zero or known, then choose the path equation that matches; verify gamma = Cp/Cv > 1 and confirm the computed work plus heat change equals delta-U before finalizing.
In interference and diffraction problems, using the slit separation or slit width and the screen distance without checking the small-angle condition, and mixing the fringe-order formula d sin(theta) = m*lambda with the single-slit minimum condition a sin(theta) = m*lambda.
Double-slit and single-slit setups look nearly identical in wording, and the small-angle approximation sin(theta) ≈ tan(theta) ≈ y/L is applied even when the computed angle exceeds about 10 degrees, silently biasing fringe positions.
What to do instead
Identify whether the problem concerns two coherent sources (maxima at d sin(theta) = mlambda) or one finite aperture (minima at a sin(theta) = mlambda); compute theta explicitly with arcsin, and only use y = mL*lambda/d when theta is small, stating that check.
Applying Kirchhoff's loop rule while ignoring the internal resistance of a source or the direction of current through a battery, so the sign of the EMF term in the loop equation is wrong and the solved current comes out negative without comment.
Circuit diagrams show batteries as ideal symbols, and candidates memorize 'sum of voltage drops equals zero' without tracking that traversing a source from negative to positive terminal adds EMF rather than subtracting a drop; internal resistance is easily overlooked when not drawn.
What to do instead
Adopt a fixed sign convention before writing equations (choose a loop direction, treat EMF as positive when traversed from - to +), explicitly include any stated internal resistance as a series resistor, and interpret a negative result as reversed current direction rather than an error.
Solving the infinite square well or hydrogen atom by quoting E_n proportional to n^2 without tracking the n = 1 ground state, so transition energies are computed as differences of adjacent levels when the question asks for a specific n-to-m jump, and photon wavelengths are inverted.
The Rydberg and particle-in-a-box formulas are memorized in several rearranged forms, and candidates lose track of whether the expression gives energy, frequency, or wavelength, especially when the level indices are not consecutive.
What to do instead
Always write the energy expression with explicit indices (E_n = -13.6 eV/n^2 for hydrogen), compute both level energies separately, subtract to get the photon energy, then convert with E = hc/lambda showing the constant's units; check that larger jumps give shorter wavelengths.
Adding velocities with the Galilean rule u' = u - v in a relativistic problem, or applying the time-dilation factor gamma in the wrong frame, so a speed exceeding c or a dilated time shorter than the proper time appears.
Everyday intuition and non-relativistic coursework make simple velocity addition automatic, and the symmetry of the Lorentz factor hides which observer measures the proper time, so candidates multiply or divide by gamma arbitrarily.
What to do instead
Use the relativistic velocity-addition formula u' = (u - v)/(1 - uv/c^2) whenever speeds are a significant fraction of c, and identify the proper time as the interval measured by the clock present at both events before choosing to multiply by gamma.
Computing stellar luminosity or surface temperature from L = 4*pi*R^2*sigma*T^4 by inserting the solar radius and solar temperature but expecting a luminosity in watts without converting, or confusing the Stefan-Boltzmann law with the Wien displacement law when asked for peak wavelength.
Stellar-structure problems blend radius, temperature, and luminosity in solar units, and the two blackbody laws are both short formulas involving T, so candidates reach for whichever was studied most recently rather than matching the law to the requested quantity.
What to do instead
Decide first whether the question asks for total flux (Stefan-Boltzmann, T^4) or peak wavelength (Wien, lambda_max = b/T), then work in solar units and convert once at the end using Lsun = 3.83e26 W and Rsun = 6.96e8 m.
Using Hubble's law v = H0*d with a redshift-derived velocity but a distance in Mpc and a Hubble constant in km/s/Mpc without unit reconciliation, or treating the result as a true recession speed at cosmological distances where peculiar velocities and expansion geometry matter.
Hubble's law is deceptively simple, and the mixed units (km, Mpc, s) invite arithmetic slips; at large z the linear law is only approximate, and candidates apply it uncritically to high-redshift objects.
What to do instead
Keep H0 in km/s/Mpc and d in Mpc so the units cancel to km/s, and restrict the linear Hubble relation to low redshift (z much less than 1); for larger z, state that a cosmological model is required and use the appropriate distance measure.
Reporting a final experimental result with more significant figures than the data support, or adding statistical and systematic uncertainties in quadrature as if they were independent random errors.
Calculators and software return many digits, and the distinction between random and systematic uncertainty is glossed over in lab practice, so candidates treat all error bars as combinable by root-sum-square.
What to do instead
Round the result to the precision of the least precise input and quote uncertainty to one or two significant figures; combine independent random errors in quadrature but add systematic errors linearly or state the dominant one separately, justifying the choice.
Fitting a straight line to data by eye or by unweighted least squares when the points have very different error bars, then quoting the slope's uncertainty from the software default without checking residuals for curvature.
Candidates equate 'linear fit' with 'press the trendline button', and plotting tools default to unweighted fits that let a single precise point dominate or a single outlier distort the slope; residual structure is rarely inspected.
What to do instead
Use weighted least squares with weights 1/sigma_i^2 when uncertainties are given, plot residuals against the independent variable to check for curvature or outliers, and report the slope with its standard error plus the reduced chi-squared as a goodness-of-fit indicator.