where
${R}_{0}$ is the activity at
$t=0$ . This equation shows exponential decay of radioactive nuclei. For example, if a source originally has a 1.00-mCi activity, it declines to 0.500 mCi in one half-life, to 0.250 mCi in two half-lives, to 0.125 mCi in three half-lives, and so on. For times other than whole half-lives, the equation
$R={R}_{0}{e}^{-\mathrm{\lambda t}}$ must be used to find
$R$ .
Phet explorations: alpha decay
Watch alpha particles escape from a polonium nucleus, causing radioactive alpha decay. See how random decay times relate to the half life.
Test prep for ap courses
A radioactive sample has N atoms initially. After 3 half-lives have elapsed, how many atoms remain?
When
${}_{84}{}^{215}\text{P}\text{o}$ decays, the product is
${}_{82}{}^{211}\text{P}\text{b.}$ The half-life of this decay process is 1.78 ms. If the initial sample contains 3.4 x 10
^{17} parent nuclei, how many are remaining after 35 ms have elapsed? What kind of decay process is this (alpha, beta, or gamma)?
This must be alpha decay since 4 nucleons (2 positive charges) are lost from the parent nucleus. The number remaining is found from:
Half-life
${t}_{1/2}$ is the time in which there is a 50% chance that a nucleus will decay. The number of nuclei
$N$ as a function of time is
$N={N}_{0}{e}^{-\mathrm{\lambda t}},$
where
${N}_{0}$ is the number present at
$t=0$ , and
$\lambda $ is the decay constant, related to the half-life by
$\lambda =\frac{0\text{.}\text{693}}{{t}_{1/2}}.$
One of the applications of radioactive decay is radioactive dating, in which the age of a material is determined by the amount of radioactive decay that occurs. The rate of decay is called the activity
$R$ :
$R=\frac{\text{\Delta}N}{\text{\Delta}t}.$
The SI unit for
$R$ is the becquerel (Bq), defined by
$\text{1 Bq}=\text{1 decay/s.}$
$R$ is also expressed in terms of curies (Ci), where
The activity
$R$ of a source is related to
$N$ and
${t}_{1/2}$ by
$R=\frac{0\text{.}\text{693}N}{{t}_{1/2}}.$
Since
$N$ has an exponential behavior as in the equation
$N={N}_{0}{e}^{-\mathrm{\lambda t}}$ , the activity also has an exponential behavior, given by
$R={R}_{0}{e}^{-\mathrm{\lambda t}},$
where
${R}_{0}$ is the activity at
$t=0$ .
Conceptual questions
In a
$3\times {\text{10}}^{9}$ -year-old rock that originally contained some
${}^{\text{238}}\text{U}$ , which has a half-life of
$4.5\times {\text{10}}^{9}$ years, we expect to find some
${}^{\text{238}}\text{U}$ remaining in it. Why are
${}^{\text{226}}\text{Ra}$ ,
${}^{\text{222}}\text{Rn}$ , and
${}^{\text{210}}\text{Po}$ also found in such a rock, even though they have much shorter half-lives (1600 years, 3.8 days, and 138 days, respectively)?
Does the number of radioactive nuclei in a sample decrease to
exactly half its original value in one half-life? Explain in terms of the statistical nature of radioactive decay.
Radioactivity depends on the nucleus and not the atom or its chemical state. Why, then, is one kilogram of uranium more radioactive than one kilogram of uranium hexafluoride?
Spontaneous radioactive decay occurs only when the decay products have less mass than the parent, and it tends to produce a daughter that is more stable than the parent. Explain how this is related to the fact that more tightly bound nuclei are more stable. (Consider the binding energy per nucleon.)
the same behavior thru the prism out or in water bud abbot
Ju
If this will experimented with a hollow(vaccum) prism in water then what will be result ?
Anurag
What was the previous far point of a patient who had laser correction that reduced the power of her eye by 7.00 D, producing a normal distant vision power of 50.0 D for her?
What is the far point of a person whose eyes have a relaxed power of 50.5 D?
Jaydie
What is the far point of a person whose eyes have a relaxed power of 50.5 D?
Jaydie
A young woman with normal distant vision has a 10.0% ability to accommodate (that is, increase) the power of her eyes. What is the closest object she can see clearly?
Jaydie
29/20 ? maybes
Ju
In what ways does physics affect the society both positively or negatively
Propose a force standard different from the example of a stretched spring discussed in the text. Your standard must be capable of producing the same force repeatedly.