Sodium-24 (1124Na^{24}_{11}\text{Na}1124Na) is produced by irradiating the stable isotope 1123Na^{23}_{11}\text{Na}1123Na with neutrons in a nuclear reactor. Each nucleus of 1124Na^{24}_{11}\text{Na}1124Na then decays into a nucleus of magnesium (Mg\text{Mg}Mg) by the emission of a beta-minus particle, one other particle, and a gamma photon.
Complete the nuclear equations for these two processes:
1123Na+......n→ 1124Na → ......Mg+......e+......+γ ^{23}_{11}\text{Na} + {^{...}_{...}}\text{n} \rightarrow\ ^{24}_{11}\text{Na}\ \rightarrow\ {^{...}_{...}}\text{Mg} + {^{...}_{...}}\text{e} + \text{......} + \gamma 1123Na+......n→ 1124Na → ......Mg+......e+......+γStudents carry out an investigation into gamma photon absorption by placing sheets of copper between a 1124Na^{24}_{11}\text{Na}1124Na source and a radiation detector. The total thickness of the copper sheets is ddd (measured in meters).
The 1124Na^{24}_{11}\text{Na}1124Na source emits beta-minus radiation as well as gamma radiation. Explain why this beta-minus radiation would not affect the experiment when copper sheets are used.
The count rate of gamma photons CCC detected in 15 minutes for a thickness d=40 mmd = 40\text{ mm}d=40 mm of copper is recorded as C=380±45C = 380 \pm 45C=380±45. The relationship between CCC and ddd is given by C=C0e−μdC = C_0 e^{-\mu d}C=C0e−μd where C0C_0C0 and μ\muμ are constants.
Show that a plot of lnC\ln ClnC against ddd gives a straight line with gradient =−μ= -\mu=−μ and y-intercept =lnC0= \ln C_0=lnC0.
Calculate the missing value of lnC\ln ClnC, including its absolute uncertainty, for C=380±45C = 380 \pm 45C=380±45. Show your calculation of the uncertainty.
In a plot of lnC\ln ClnC against the thickness ddd (in meters), the student determines the gradient of the best-fit line to be −35.0 m−1-35.0\text{ m}^{-1}−35.0 m−1 and the gradient of the worst-fit line to be −38.2 m−1-38.2\text{ m}^{-1}−38.2 m−1. Use these values to find the linear attenuation coefficient μ\muμ of copper in m−1\text{m}^{-1}m−1, including its absolute uncertainty.
Using your best-fit value of μ=35.0 m−1\mu = 35.0\text{ m}^{-1}μ=35.0 m−1, calculate the half-value thickness d1/2d_{1/2}d1/2 of copper in meters.
90 exam-style questions on OCR A A Level Physics Nuclear and particle physics, covering The nuclear atom, Fundamental particles, Radioactivity, and Nuclear fission and fusion. Each one has a worked solution and a mark scheme showing where the marks go.