Radioactivity Flashcards

Question

How can the random nature of radioactive decay be proven?

Answer 1

The random nature of radioactive decay can be demonstrated by observing the count rate of a Geiger-Muller (GM) tube When a GM tube is placed near a radioactive source, the counts are found to be irregular and cannot be predicted Each count represents a decay of an unstable nucleus These fluctuations in count rate on the GM tube provide evidence for the randomness of radioactive decay.

Answer 2

Since radioactive decay is spontaneous and random, it is useful to consider the average number of nuclei that are expected to decay per unit time This is known as the average decay rate.

Answer 3

The decay constant λ is defined as: The probability that an individual nucleus will decay per unit of time.

Answer 4

Activity, or the number of decays per unit time

Answer 5

A=ΔN/Δt=-(Lambda)N A = activity of the sample (Bq) ΔN = number of decayed nuclei Δt = time interval (s) λ = decay constant (s-1) N = number of nuclei remaining in a sample

Answer 6

The activity of a sample is measured in Becquerels (Bq) An activity of 1 Bq is equal to one decay per second, or 1 s-1

Answer 7

The greater the decay constant, the greater the activity of the sample The activity depends on the number of undecayed nuclei remaining in the sample The minus sign indicates that the number of nuclei remaining decreases with time. However, for calculations it can be omitted

Answer 8

In radioactive decay, the number of undecayed nuclei falls very rapidly, without ever reaching zero Such a model is known as exponential decay. **The key features of this graph are:** The steeper the slope, the larger the decay constant λ (and vice versa) The decay curves always start on the y-axis at the initial number of undecayed nuclei (N0) | Graph is in the document

Answer 9

X=X0e^-λt X can be A,N or C C = count rate at a certain time t (counts per minute or cpm) A = activity at a certain time t (Bq) N = number of undecayed nuclei at a certain time t

Answer 10

Avogadro’s constant (NA) is defined as: The number of atoms in one mole of a substance; equal to 6.02 × 1023 mol-1

Answer 11

n=N/NA=M/Mr M = Mass (g) Mr= Molar mass (g mol^-1) N= Number of Nuclei NA=Avogradro's constant (mol^-1)

Answer 12

The time taken for the initial number of nuclei to halve for a particular isotope.

Answer 13

t(1/2) = ln2/λ

Answer 14

Straight-line graphs tend to be more useful than curves for interpreting data Nuclei decay exponentially, therefore, to achieve a straight line plot, logarithms can be used.

Answer 15

The isotope carbon-14 is commonly used in radioactive dating It forms as a result of cosmic rays knocking out neutrons from nuclei, which then collide with nitrogen nuclei in the air: 1 n + 14N → 14C + 1 p Plants take in carbon dioxide from the atmosphere for photosynthesis, including the radioactive isotope carbon-14 Animals and humans take in carbon-14 by eating the plants Therefore, all living organisms absorb carbon-14, but after they die they do not absorb any more The proportion of carbon-14 is constant in living organisms as carbon is constantly being replaced during the period they are alive When they die, the activity of carbon-14 in the organic matter starts to fall, with a half-life of around 5730 years Samples of living material can be tested by comparing the current amount of carbon-14 in them and compared to the initial amount (which is based on the current ratio of carbon-14 to carbon-12), and hence they can be dated.

Answer 16

Carbon dating is a highly reliable ageing method for samples ranging from around 1000 years old up to a limit of around 40 000 years old Therefore, for very young, or very old samples, carbon dating is not the most reliable method to use This can be explained by looking at the decay curve of carbon-14: If the sample is less than 1000 years old: The activity of the sample will be too high So, it is difficult to accurately measure the small change in activity Therefore, the ratio of carbon-14 to carbon-12 will be too high to determine an accurate age If the sample is more than 40 000 years old: The activity will be too small and have a count rate similar to that of background radiation So, there will be very few carbon-14 atoms remaining, hence very few decays will occur Therefore, the ratio of carbon-14 to carbon-12 will be too small to determine an accurate age Carbon dating uses the currently known ratio of carbon-14 to carbon-12, however, scientists cannot know the level of carbon-14 in the biosphere thousands of years ago Therefore, this makes it difficult to age samples which are very old.

Answer 17

Ancient rocks contain trapped argon gas as a result of the decay of the radioactive isotope of potassium-40 This happens when a potassium nucleus captures an inner shell electron, also known as electron capture 40K + e– → 40Ar + ve The potassium isotope can also decay by β– emission to form calcium-40 40K → 40Ca + β– + vₑ The half-life of the potassium-40 is 1.25 billion years The age of the rock (when it solidified) can be calculated by measuring the proportion of argon-40 to potassium-40 This method is accurate for dating rocks up to 100 million years old.

Answer 18

While the potassium-argon method is best for ageing younger rocks, the uranium-lead method has been critical in dating geologic events more than 100 million years old Initially, there is only uranium in the rock, but over time, the uranium decays via a decay chain which ends with lead-206, which is a stable isotope Uranium has a half-life of 4.5 billion years and over time, the ratio of lead-206 atoms to uranium-238 atoms increases This ratio may be used to determine the age of a sample of rock Uranium is so well studied that its decay constant is much better known than other isotopes, such as potassium, making the uranium-lead dating technique the most accurate available

Answer 19

Radioactive substances can be dangerous and some substances have very long half-lives (even billions of years) This means that they will be emitting harmful radiation well above background radiation for a very long time Waste products from nuclear power stations need to be appropriately stored for the remaining time that they are radioactive Common methods are water tanks or sealed underground This is to prevent damage to people and the environment now and for many years into the future Sealing them underground means they are less likely to be dislodged or released due to natural disasters.

Answer 20

P =ΔE/Δt = AE | This is the energy transfer per second from a radioactive source

Answer 21

The most common elements in the universe all tend to have values of N and Z less than 20 (plus iron which has Z = 26, N = 30) Where: N = number of neutrons Z = number of protons / atomic number This is because lighter elements (with fewer protons) tend to be much more stable than heavier ones (with many protons)

Answer 22

A nucleus will be unstable if it has: Too many neutrons Too many protons Too many nucleons ie. too heavy Too much energy An unstable atom wants to become neutral to become stable

Answer 23

For light isotopes, Z < 20: All these nuclei tend to be very stable They follow the straight-line N = Z For heavy isotopes, Z > 20: The neutron-proton ratio increases Stable nuclei must have more neutrons than protons

Answer 24

This imbalance in the neutron-proton ratio is very significant to the stability of nuclei At a short-range (around 1–4 fm), nucleons are bound by the strong nuclear force Below 1 fm, the strong nuclear force is repulsive in order to prevent the nucleus from collapsing At longer ranges, the electromagnetic force acts between protons, so more protons cause more instability Therefore, as more protons are added to the nucleus, more neutrons are needed to add distance between protons to reduce the electrostatic repulsion Also, the extra neutrons increase the amount of binding force which helps to bind the nucleons together.

Answer 25

Alpha-emitters: Occur beneath the line of stability when Z > 60 where there are too many nucleons in the nucleus These nuclei have more neutrons than protons, but they are too large to be stable This is because the strong nuclear force between the nucleons is unable to overcome the electrostatic force of repulsion between the protons.

Answer 26

Beta-minus (β– ) emitters: Occur to the left of the stability line where the isotopes are neutron-rich compared to stable isotopes A neutron is converted to a proton and emits a β– particle (and an anti-electron neutrino)

Answer 27

Beta-plus (β+ ) emitters: Occur to the right of the stability line where the isotopes are proton-rich compared to stable isotopes A proton is converted to a neutron and emits a β+ particle (and an electron neutrino)

Answer 28

When a nucleus captures one of its own orbiting electrons As with β+ decay, a proton in the nucleus is converted into a neutron, releasing a gamma-ray (and an electron neutrino) Hence, this also occurs to the right of the stability line where the isotopes are proton-rich compared to stable isotope.

Answer 29

Decays through gamma (γ) emission A gamma particle is a high-energy electromagnetic radiation This usually occurs after a different type of decay, such as alpha or beta decay This is because the nucleus becomes excited and has excess energy.

Answer 30

In the same way that electrons can exist in excited states, nuclei can also exist in excited states After an unstable nucleus emits an alpha particle, beta particle or undergoes electron capture, it may emit any remaining energy in the form of a gamma photon (γ) Emission of a γ photon does not change the number of protons or neutrons in the nucleus, it only allows the nucleus to lose energy This happens when a daughter nucleus is in an excited state after a decay This excited state is usually very short-lived, and the nucleus quickly moves to its ground state, either directly or via one or more lower-energy excited states One common application of this is the use of technetium-99m as a γ source in medical diagnosis The ‘m’ stands for metastable which means the nucleus exists in a particularly stable excited state Technetium-99m is the decay product of molybdenum-99, which can be found as a product in nuclear reactors.

Answer 31

In the Rutherford scattering experiment, alpha particles are fired at a thin gold foil Some of the alpha particles are found to come straight back from the gold foil This indicates that there is electrostatic repulsion between the alpha particles and the gold nucleus At the point of closest approach, r, the repulsive force reduces the speed of the alpha particles to zero momentarily At this point, the initial kinetic energy of an alpha particle, Ek , is equal to electric potential energy, Ep The radius of the closest approach can be found be equating the initial kinetic energy to the electric potential energy.

Answer 32

Alpha scattering gives a good estimate of the upper limit for a nuclear radius The mathematics behind this approach are very simple The alpha particles are scattered only by the protons and not all the nucleons that make up the nucleus.

Answer 33

This method does not give an accurate value for nuclear radius as it will always be an overestimate This is because it measures the nearest distance the alpha particle can get to the gold nucleus, not the radius of it Alpha particles are hadrons, therefore, when they get close to the nucleus they are affected by the strong nuclear force and the mathematics do not account for this The gold nucleus will recoil as the alpha particle approaches Alpha particles have a finite size whereas electrons can be treated as a point mass It is difficult to obtain alpha particles which rebound at exactly 180° In order to do this, a small collision region is required The alpha particles in the beam must all have the exact same initial kinetic energy The sample must be extremely thin to prevent multiple scattering.

Answer 34

Electrons accelerated to close to the speed of light have wave-like properties such as the ability to diffract and have a de Broglie wavelength. The diffraction pattern forms a central bright spot with dimmer concentric circles around it From this pattern, a graph of intensity against diffraction angle can be used to find the diffraction angle of the first minimum.

Answer 35

Electron diffraction is much more accurate than the closest approach method This method gives a direct measurement of the radius of a nucleus Electrons are leptons; therefore, they will not interact with nucleons in the nucleus through the strong nuclear force as an alpha particle would.

Answer 36

Electrons must be accelerated to very high speeds to minimise the de Broglie wavelength and increase resolution This is because significant diffraction takes place when the electron wavelength is similar in size to the nuclear diameter Electrons can be scattered by both protons and neutrons If there is an excessive amount of scattering, then the first minimum of the electron diffraction can be difficult to determine.

Answer 37

λ=h/mv h = Planck's constant m = mass of an electron (kg) v = speed of the electrons (m s−1)

Answer 38

sinθ=1.22λ/2R θ = angle of the first minimum (degrees) λ = de Broglie wavelength (m) R = radius of the nucleus (m)

Answer 39

10^-15 or 1fm

Answer 40

The key features of this graph are: The graph starts with a steep gradient at the origin Then the gradient gradually decreases to almost horizontal This means that As more nucleons are added to a nucleus, the nucleus gets bigger However, the number of nucleons A is not proportional to its size r | Graph found in document

Answer 41

R=R0A^(1/3) R = nuclear radius (m) A = nucleon / mass number R0 = constant of proportionality = 1.05 fm

Answer 42

The graph is provided in the document

Answer 43

Therefore, a graph of ln R against ln A yields a straight line Comparing this to the straight-line equation: y = mx + c y = lnR x = lnA m (the gradient) = 1/3 c (y-intercept) = ln R0 | Graph provided in the document

Answer 44

Get the equation

Answer 45

ρ=3u/4π(R0)^3 Atomic mass unit, u = 1.661 × 10–27 kg Constant of proportionality, R0 = 1.05 × 10–15 m

Answer 46

Since the mass number A cancels out, the remaining quantities in the equation are all constant Therefore, this shows the density of the nucleus is: Constant Independent of the radius The fact that nuclear density is constant shows that nucleons are evenly separated throughout the nucleus regardless of their size

Answer 47

Nuclear density is significantly larger than atomic density, this suggests: The majority of the atom’s mass is contained in the nucleus The nucleus is very small compared to the atom Atoms must be predominantly empty space