A Geiger-Müller (G-M) tube is a device that can detect beta-radiation. A student places paper between a radioactive source emitting beta-radiation and a G-M tube, as shown in Fig. 2.1. The G-M tube is connected to a rate-meter which records the count rate R. The thickness t of the paper is measured in two different places using a micrometer. The student repeats the experiment for different thicknesses of paper. It is suggested that R and t are related by the equation R = R₀e⁻µⁿ where R₀ is the count rate without any paper and µ is a constant.

Mark scheme

Marking points from the official mark scheme (Oct/Nov 2021). The mark or mark type is shown in brackets.

1. [1] gradient = -µ y-intercept = In R₀
2. [1] Values of average t and In R correct as shown above.
3. [1] Absolute uncertainties in average t correct as shown above.
4. [1] Six points plotted correctly. Must be accurate to nearest half a small square. Diameter of points must be less than half a small square.
5. [1] Error bars in average t plotted correctly. All error bars must be plotted. Total length of bar must be accurate to less than half a small square and symmetrical.
6. [1] Line of best fit drawn. Points must be balanced. Do not accept line from top point to bottom point. Line must pass between (0.22, 3.80) and (0.24, 3.80) and between (0.60, 3.50) and (0.62, 3.50).
7. [1] Worst acceptable line drawn (steepest or shallowest possible line that passes through all error bars). All error bars must be plotted.
8. [1] Negative gradient determined with clear substitution of data points into Δy / Δx. Distance between data points must be at least half the length of the drawn line.
9. [1] Gradient of worst acceptable line determined.
10. [1] uncertainty = (gradient of line of best fit – gradient of worst acceptable line) or uncertainty = ½ (steepest worst line gradient – shallowest worst line gradient)
11. [1] y-intercept determined by substitution of point on line into y = mx + c.
12. [1] y-intercept of worst acceptable line determined by substitution of point on line into y = mx + c.
13. [1] uncertainty = y-intercept of line of best fit – y-intercept of worst acceptable line or uncertainty = ½ (steepest worst line y-intercept – shallowest worst line y-intercept)
14. [1] µ = – gradient value. Do not accept negative values (from a negative gradient).
15. [1] R₀ determined using y-intercept and µ and R₀ both given with valid SI unit. R₀ = e^(y-intercept)
16. [1] unit of µ: mm⁻¹ unit of R₀: s⁻¹
17. [1] absolute uncertainty in µ = absolute uncertainty in gradient and absolute uncertainty in R₀ = e^(y-intercept of WAL) – R₀. Correct substitution of numbers must be seen.
18. [1] Value of t determined to two or three significant figures from (d) or (c)(iii) and (c)(iv) with correct substitution and correct power of ten(s). t = (In R – In R₀) / –µ or t = (In 20 - y-intercept) / gradient