# 30.5 Half-life and activity  (Page 8/16)

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(a) The ${}^{\text{210}}\text{Po}$ source used in a physics laboratory is labeled as having an activity of $1.0\phantom{\rule{0.25em}{0ex}}\mu \text{Ci}$ on the date it was prepared. A student measures the radioactivity of this source with a Geiger counter and observes 1500 counts per minute. She notices that the source was prepared 120 days before her lab. What fraction of the decays is she observing with her apparatus? (b) Identify some of the reasons that only a fraction of the $\alpha$ s emitted are observed by the detector.

(a) $\text{1.23}×{\text{10}}^{-3}$

(b) Only part of the emitted radiation goes in the direction of the detector. Only a fraction of that causes a response in the detector. Some of the emitted radiation (mostly $\alpha$ particles) is observed within the source. Some is absorbed within the source, some is absorbed by the detector, and some does not penetrate the detector.

Armor-piercing shells with depleted uranium cores are fired by aircraft at tanks. (The high density of the uranium makes them effective.) The uranium is called depleted because it has had its ${}^{\text{235}}\text{U}$ removed for reactor use and is nearly pure ${}^{\text{238}}\text{U}$ . Depleted uranium has been erroneously called non-radioactive. To demonstrate that this is wrong: (a) Calculate the activity of 60.0 g of pure ${}^{\text{238}}\text{U}$ . (b) Calculate the activity of 60.0 g of natural uranium, neglecting the ${}^{\text{234}}\text{U}$ and all daughter nuclides.

The ceramic glaze on a red-orange Fiestaware plate is ${\text{U}}_{2}{\text{O}}_{3}$ and contains 50.0 grams of ${}^{238}\text{U}$ , but very little ${}^{235}\text{U}$ . (a) What is the activity of the plate? (b) Calculate the total energy that will be released by the ${}^{238}\text{U}$ decay. (c) If energy is worth 12.0 cents per $\text{kW}\cdot \text{h}$ , what is the monetary value of the energy emitted? (These plates went out of production some 30 years ago, but are still available as collectibles.)

(a) $1.68×{10}^{–5}\phantom{\rule{0.25em}{0ex}}\text{Ci}$

(b) $8.65×{10}^{10}\phantom{\rule{0.25em}{0ex}}\text{J}$

(c) $2.9×{10}^{3}$

Large amounts of depleted uranium ( ${}^{238}\text{U}$ ) are available as a by-product of uranium processing for reactor fuel and weapons. Uranium is very dense and makes good counter weights for aircraft. Suppose you have a 4000-kg block of ${}^{238}\text{U}$ . (a) Find its activity. (b) How many calories per day are generated by thermalization of the decay energy? (c) Do you think you could detect this as heat? Explain.

The Galileo space probe was launched on its long journey past several planets in 1989, with an ultimate goal of Jupiter. Its power source is 11.0 kg of ${}^{238}\text{Pu}$ , a by-product of nuclear weapons plutonium production. Electrical energy is generated thermoelectrically from the heat produced when the 5.59-MeV $\text{α}$ particles emitted in each decay crash to a halt inside the plutonium and its shielding. The half-life of ${}^{238}\text{Pu}$ is 87.7 years. (a) What was the original activity of the ${}^{238}\text{Pu}$ in becquerel? (b) What power was emitted in kilowatts? (c) What power was emitted 12.0 y after launch? You may neglect any extra energy from daughter nuclides and any losses from escaping $\text{γ}$ rays.

(a) $6.97×{10}^{15}\phantom{\rule{0.25em}{0ex}}\text{Bq}$

(b) 6.24 kW

(c) 5.67 kW

Consider the generation of electricity by a radioactive isotope in a space probe, such as described in [link] . Construct a problem in which you calculate the mass of a radioactive isotope you need in order to supply power for a long space flight. Among the things to consider are the isotope chosen, its half-life and decay energy, the power needs of the probe and the length of the flight.

Unreasonable Results

A nuclear physicist finds $1.0\phantom{\rule{0.25em}{0ex}}\mu \text{g}$ of ${}^{236}\text{U}$ in a piece of uranium ore and assumes it is primordial since its half-life is $2.3×{10}^{7}\phantom{\rule{0.25em}{0ex}}\text{y}$ . (a) Calculate the amount of ${}^{236}\text{U}$ that would had to have been on Earth when it formed $4.5×{10}^{9}\phantom{\rule{0.25em}{0ex}}\text{y}$ ago for $1.0\phantom{\rule{0.25em}{0ex}}\mu \text{g}$ to be left today. (b) What is unreasonable about this result? (c) What assumption is responsible?

Unreasonable Results

(a) Repeat [link] but include the 0.0055% natural abundance of ${}^{234}\text{U}$ with its $2.45×{10}^{5}\phantom{\rule{0.25em}{0ex}}\text{y}$ half-life. (b) What is unreasonable about this result? (c) What assumption is responsible? (d) Where does the ${}^{234}\text{U}$ come from if it is not primordial?

Unreasonable Results

The manufacturer of a smoke alarm decides that the smallest current of $\text{α}$ radiation he can detect is $1.00\phantom{\rule{0.25em}{0ex}}\mu \text{A}$ . (a) Find the activity in curies of an $\text{α}$ emitter that produces a $1.00\phantom{\rule{0.25em}{0ex}}\mu \text{A}$ current of $\text{α}$ particles. (b) What is unreasonable about this result? (c) What assumption is responsible?

(a) 84.5 Ci

(b) An extremely large activity, many orders of magnitude greater than permitted for home use.

(c) The assumption of $1.00\phantom{\rule{0.25em}{0ex}}\text{μA}$ is unreasonably large. Other methods can detect much smaller decay rates.

find the 15th term of the geometric sequince whose first is 18 and last term of 387
I know this work
salma
The given of f(x=x-2. then what is the value of this f(3) 5f(x+1)
hmm well what is the answer
Abhi
how do they get the third part x = (32)5/4
can someone help me with some logarithmic and exponential equations.
20/(×-6^2)
Salomon
okay, so you have 6 raised to the power of 2. what is that part of your answer
I don't understand what the A with approx sign and the boxed x mean
it think it's written 20/(X-6)^2 so it's 20 divided by X-6 squared
Salomon
I'm not sure why it wrote it the other way
Salomon
I got X =-6
Salomon
ok. so take the square root of both sides, now you have plus or minus the square root of 20= x-6
oops. ignore that.
so you not have an equal sign anywhere in the original equation?
hmm
Abhi
is it a question of log
Abhi
🤔.
Abhi
I rally confuse this number And equations too I need exactly help
salma
But this is not salma it's Faiza live in lousvile Ky I garbage this so I am going collage with JCTC that the of the collage thank you my friends
salma
Commplementary angles
hello
Sherica
im all ears I need to learn
Sherica
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Tamia
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Uday
hi
salma
what is a good calculator for all algebra; would a Casio fx 260 work with all algebra equations? please name the cheapest, thanks.
a perfect square v²+2v+_
kkk nice
algebra 2 Inequalities:If equation 2 = 0 it is an open set?
or infinite solutions?
Kim
The answer is neither. The function, 2 = 0 cannot exist. Hence, the function is undefined.
Al
y=10×
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Kristine 2*2*2=8
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what's the easiest and fastest way to the synthesize AgNP?
China
Cied
types of nano material
I start with an easy one. carbon nanotubes woven into a long filament like a string
Porter
many many of nanotubes
Porter
what is the k.e before it land
Yasmin
what is the function of carbon nanotubes?
Cesar
I'm interested in nanotube
Uday
what is nanomaterials​ and their applications of sensors.
what is nano technology
what is system testing?
preparation of nanomaterial
Yes, Nanotechnology has a very fast field of applications and their is always something new to do with it...
what is system testing
what is the application of nanotechnology?
Stotaw
In this morden time nanotechnology used in many field . 1-Electronics-manufacturad IC ,RAM,MRAM,solar panel etc 2-Helth and Medical-Nanomedicine,Drug Dilivery for cancer treatment etc 3- Atomobile -MEMS, Coating on car etc. and may other field for details you can check at Google
Azam
anybody can imagine what will be happen after 100 years from now in nano tech world
Prasenjit
after 100 year this will be not nanotechnology maybe this technology name will be change . maybe aftet 100 year . we work on electron lable practically about its properties and behaviour by the different instruments
Azam
name doesn't matter , whatever it will be change... I'm taking about effect on circumstances of the microscopic world
Prasenjit
how hard could it be to apply nanotechnology against viral infections such HIV or Ebola?
Damian
silver nanoparticles could handle the job?
Damian
not now but maybe in future only AgNP maybe any other nanomaterials
Azam
Hello
Uday
I'm interested in Nanotube
Uday
this technology will not going on for the long time , so I'm thinking about femtotechnology 10^-15
Prasenjit
can nanotechnology change the direction of the face of the world
At high concentrations (>0.01 M), the relation between absorptivity coefficient and absorbance is no longer linear. This is due to the electrostatic interactions between the quantum dots in close proximity. If the concentration of the solution is high, another effect that is seen is the scattering of light from the large number of quantum dots. This assumption only works at low concentrations of the analyte. Presence of stray light.
the Beer law works very well for dilute solutions but fails for very high concentrations. why?
how did you get the value of 2000N.What calculations are needed to arrive at it
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