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aqa A-level physics
Year 2 (yr13)
radioactive decay: chapter 11
Decay models of unstable nuclei
Alpha α |
Beta minus β- |
Beta plus β+ |
Gamma γ |
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N decay to P, emitting e and /Ve |
(K capture) |
nucleu in excited state emits photon-some after β decay |
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6328
Ni -> 6329
Cu + -1
e + /Ve |
12453
I +1
e-> 12452
Te + Ve |
9942
Mo -> 99m43
Tc + -1
e + /Ve |
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m -> metastable state |
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nucleus in high excited state for extended time |
time (grater than a billionth of a second) |
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Equations
decay rate |
∆N/∆t = -λN |
activity |
A = λN |
half life |
T = ln2/λ |
activity |
ln2N/T |
Number of atoms after decay |
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activity after decay |
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mass |
mol x RAM |
Definitions
spontaneous |
can't be influenced/independent |
random |
can't predict when it will happen |
decay constant |
probability of a nucleus decaying per unit time |
activity |
number of disintegrations (or emissions) per unit time |
metastable state |
when an atom/nucleus exists for an extended time in a state other than ground state |
daughter nucleus |
product of the decay of a radioactive ('parent') nucleus |
half life |
time taken for half of a sample of radioactive nuclei to decay |
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radioactive decay
--> the significance of the - sign in -λN is that the number of radioactive nuclei in a sample material decreases over time
Example Question:
. Lanthanum-139 is the more abundant
isotope and makes up 99.911% of naturally occurring lanthanum. The remaining 0.089% is the radioisotope lanthanum-138
. Lanthanum-138 has a decay constant of 2.0 × 10−19 s−1; and 139g of lanthanum contain 6 × 10^23 atoms.
Calculate the activity of a 40g sample of Lanthanum
The number of atoms in 40g of lanthanum is
6 x1023 x 40/139 = 1.73 x1023
However, only 0.089% of these are lanthanum-138.
So the number of lanthanum-138 nuclei is
N = 1.73x1023 x 0.089/100 = 1.54x1020
so
A=λN
= 2.0x10-19 s-1 x 1.54x1020
= 31Bq |
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Uses of radioisotopes:
Radiotherapy |
Gamma rays γ |
- rotating source of gamma rays |
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- reduces exposure to healthy tissue |
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- focuses exposure to tumor |
Alpha rays α |
- injected directly into the tissue |
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- attach to a biological molecule (eg glucose) that needs to divide |
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- collects to the caner cells that love to divide |
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Carbon dating |
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- uses 14C (half life of 5700 years) |
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- The ratio of Carbon-14 remaining indicates the times since the death of a living substance |
Nuclear Instability
- every element has many different isotopes
- however most isotopes are unstable, and decay by emission of radiation to become more stable
- this can be plotted on a no.Neutrons to no.Protons graph |
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