1. When identifying a particular isotope of an atom, the usual symbol is preceded by the atomic weight of the isotope. Thus tritium (a radioactive isotope of hydrogen) whose atomic weight is 3, would be written 3H while the most common hydrogen isotope is 1H. The symbol for carbon, atomic weight 14, is 14C.
Write the symbol for the tin isotope with atomic weight 113.
Solution. 113Sn
2. When the nucleus of a radioactive atom undergoes a change, the atom is said to decay (to produce a different atom). Another name for this event is radioactive disintegration. Different atoms undergo decay by different processes, so the energy produced as a result of the process depends on the isotope involved.
One way of describing the quantity of a particular radioactive material is through the number of disintegrations that take place in unit time, usually seconds. The reason is that the number of disintegrations is proportional to the amount of material present. The fundamental unit is the Becquerel (Bq), which represents one disintegration per second (dps).
The becquerel is usually too small a unit for practical purposes, so kilo- or megabecquerels are more commonly used.
A. If the radioactivity of a material is 1.40 × 102kBq, how many dps does that represent?
B. Express the radioactivity of a substance with 6.33 × 107 disintegrations per second in terms of megabecquerels.
Solutions.
A. 1.4 × 10s dps
B. 63.3 MBq
CALCULATIONS
A. 1.40 × 102kBq × 1000 dps/kBq = 1.4 × 105dps
B.
3. A second unit, older but still widely used, is the curie (Ci), defined as 3.7 × 1010dps. As with other units, prefixes are used to scale the unit size and bring numerical values into a convenient range. For small quantities of radiation, millicuries or microcuries are commonly used.
A. How many disintegrations per second are represented by a material whose activity is 9.26 mCi?
B. If an isotope undergoes 107 disintegrations per minute, how many microcuries does this represent?
C. How many kBq are equivalent to 20 μCi of a radioactive substance?
Solutions.
A. 3.43 × 108dps
B. 4.51 μCi
C. 740 kBq
CALCULATIONS
A.
B.
C.
4. Disintegrations per second observed for a radioisotopes sample is proportional to the number of radioactive molecules present. The following equation applies to an individual isotope:
In this equation, N is the number of radioactive molecules at any time, t, and λ. (lambda) is a rate constant that depends on the identity of the particular substance. Using the notation of differential calculus, the rate of decay can be represented as −dN/dt. This expression describes the change in N with time; the negative sign in front of the expression indicates that as time goes on (increases), N decreases. In the absence of the negative sign, the expression would say that the amount of radioactive substance should grow over time rather than decay.
Which of the following statements are true?
A. The number of disintegrations per unit time is proportional to the amount of a given radioactive substance present.
B. The number of molecules of a given isotope decreases as time goes on.
Solution. Both statements are true.
5. Calculate λ, the decay rate constant, for an isotope if 100 kBq decays instantaneously at a rate of 0.023 MBq/year.
Solution. 0.23 year−1
CALCULATIONS
rate of decay = λN
6. In frame 5 we saw that radioactive decay could be described by this equation:
This equation can be rearranged to
and solved by integration to yield
N0 is defined as the initial number of radioactive atoms present; e is the base of natural logarithms, 2.718. Using this equation and a calculator or log table, it is possible to calculate the amount of radioactivity at any time if we know the original activity and the rate constant.
But before we do any calculations of that type, let us explore some properties of this equation by dividing both sides by N0:
The product of λ and t in this equation has to be dimensionless. Therefore the units of λ are reciprocal time (1/time). For example, if the unit of time used is seconds (s), the units of λ are expressed as 1/s usually written s−1.
Write the units for λ when time is in years.
Solution.
7. We saw that the decay equation could be written
