Flashcards · 9630 · A Level Topic 9

Exponential change (A Level) flashcards

12 cards on A Level Topic 9, subtopics 3.9.1 to 3.9.2. Pick a subtopic or study them all.

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Equations for a capacitor discharging through a resistor: Q = Q₀e^(−t/RC), V = V₀e^(−t/RC), I = I₀e^(−t/RC), with I₀ = V₀/R.
Equations for a capacitor charging through a resistor from a supply V₀: Q = Q₀(1 − e^(−t/RC)) and V = V₀(1 − e^(−t/RC)), where Q₀ = CV₀ is the final charge. The current I = I₀e^(−t/RC) falls.
Time constant, and what happens in one time constant: Time constant = RC (seconds with R in Ω and C in F). In one RC a discharging quantity falls to 0.37 (37%) of its start value; a charging capacitor reaches 0.63 of its final value.
Time to halve when a capacitor discharges: T½ = ln 2 × RC = 0.693RC, which is shorter than RC.
Finding RC from a graph of ln V against t (discharge): The graph is a straight line with gradient −1/RC, so RC = −1/gradient. The intercept is ln V₀.
What do the gradient of a Q–t graph and the area under an I–t graph give?: Gradient of Q–t: the current. Area under I–t: the charge that has flowed.

Radioactive decay is random and spontaneous. Meaning?: Random: you cannot predict which nucleus will decay or when. Spontaneous: it is not affected by external conditions such as temperature, pressure or chemical state.
Decay constant λ: The probability per unit time that a nucleus will decay. Unit s⁻¹ (or h⁻¹, y⁻¹).
Activity: definition and equation: The number of decays per second in a sample: A = λN. Unit becquerel, Bq (s⁻¹).
Exponential decay equations and half-life: N = N₀e^(−λt), A = A₀e^(−λt). T½ = ln 2/λ = 0.693/λ.
Number of nuclei in a mass m of a nuclide of molar mass M: N = (m/M) × N_A, with m in g, M in g mol⁻¹ and N_A = 6.02 × 10²³ mol⁻¹.
Finding λ from a graph of ln A against t: ln A = ln A₀ − λt: a straight line with gradient −λ. So λ = −gradient and T½ = ln 2/λ. Use corrected count rates.