# 31.4 Nuclear decay and conservation laws  (Page 8/27)

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## Section summary

• When a parent nucleus decays, it produces a daughter nucleus following rules and conservation laws. There are three major types of nuclear decay, called alpha $\left(\alpha \right),$ beta $\left(\beta \right),$ and gamma $\left(\gamma \right)$ . The $\alpha$ decay equation is
${}_{Z}^{A}{X}_{N}\to {}_{Z-2}^{A-4}{\text{Y}}_{N-2}+{}_{2}^{4}{\text{He}}_{2}.$
• Nuclear decay releases an amount of energy $E$ related to the mass destroyed $\Delta m$ by
$E=\left(\Delta m\right){c}^{2}.$
• There are three forms of beta decay. The ${\beta }^{-}$ decay equation is
${}_{Z}^{A}{X}_{N}\to {}_{Z+1}^{A}{\text{Y}}_{N-1}+{\beta }^{-}+{\overline{\nu }}_{e}.$
• The ${\beta }^{+}$ decay equation is
${}_{Z}^{A}{X}_{N}\to {}_{Z-1}^{A}{\text{Y}}_{N+1}+{\beta }^{+}+{\nu }_{e}.$
• The electron capture equation is
${}_{Z}^{A}{X}_{N}+{e}^{-}\to {}_{Z-1}^{A}{\text{Y}}_{N+1}+{\nu }_{e}.$
• ${\beta }^{-}$ is an electron, ${\beta }^{+}$ is an antielectron or positron, ${\nu }_{e}$ represents an electron’s neutrino, and ${\overline{\nu }}_{e}$ is an electron’s antineutrino. In addition to all previously known conservation laws, two new ones arise— conservation of electron family number and conservation of the total number of nucleons. The $\gamma$ decay equation is
${}_{Z}{}^{A}\text{}{\text{X}}_{N}^{*}\to {}_{Z}{}^{A}\text{}{\text{X}}_{N}+{\gamma }_{1}+{\gamma }_{2}+\cdots$
$\gamma$ is a high-energy photon originating in a nucleus.

## Conceptual questions

Star Trek fans have often heard the term “antimatter drive.” Describe how you could use a magnetic field to trap antimatter, such as produced by nuclear decay, and later combine it with matter to produce energy. Be specific about the type of antimatter, the need for vacuum storage, and the fraction of matter converted into energy.

What conservation law requires an electron’s neutrino to be produced in electron capture? Note that the electron no longer exists after it is captured by the nucleus.

Neutrinos are experimentally determined to have an extremely small mass. Huge numbers of neutrinos are created in a supernova at the same time as massive amounts of light are first produced. When the 1987A supernova occurred in the Large Magellanic Cloud, visible primarily in the Southern Hemisphere and some 100,000 light-years away from Earth, neutrinos from the explosion were observed at about the same time as the light from the blast. How could the relative arrival times of neutrinos and light be used to place limits on the mass of neutrinos?

What do the three types of beta decay have in common that is distinctly different from alpha decay?

## Problems&Exercises

In the following eight problems, write the complete decay equation for the given nuclide in the complete ${}_{Z}^{A}{X}_{N}$ notation. Refer to the periodic table for values of $Z$ .

${\beta }^{-}$ decay of ${}^{3}\text{H}$ (tritium), a manufactured isotope of hydrogen used in some digital watch displays, and manufactured primarily for use in hydrogen bombs.

${}_{1}^{3}{\text{H}}_{2}\to {}_{2}^{3}{\text{He}}_{1}+{\beta }^{-}+{\overline{\nu }}_{e}$

${\beta }^{-}$ decay of ${}^{\text{40}}K$ , a naturally occurring rare isotope of potassium responsible for some of our exposure to background radiation.

${\beta }^{+}$ decay of ${}^{\text{50}}\text{Mn}$ .

${}_{\text{25}}^{\text{50}}{M}_{\text{25}}\to {}_{\text{24}}^{\text{50}}{\text{Cr}}_{\text{26}}+{\beta }^{+}+{\nu }_{e}$

${\beta }^{+}$ decay of ${}^{\text{52}}\text{Fe}$ .

Electron capture by ${}^{7}\text{Be}$ .

${}_{4}^{7}{\text{Be}}_{3}+{e}^{-}\to {}_{3}^{7}{\text{Li}}_{4}+{\nu }_{e}$

Electron capture by ${}^{\text{106}}\text{In}$ .

$\alpha$ decay of ${}^{\text{210}}\text{Po}$ , the isotope of polonium in the decay series of ${}^{\text{238}}\text{U}$ that was discovered by the Curies. A favorite isotope in physics labs, since it has a short half-life and decays to a stable nuclide.

${}_{\text{84}}^{\text{210}}{\text{Po}}_{\text{126}}\to {}_{\text{82}}^{\text{206}}{\text{Pb}}_{\text{124}}+{}_{2}^{4}{\text{He}}_{2}$

$\alpha$ decay of ${}^{\text{226}}\text{Ra}$ , another isotope in the decay series of ${}^{\text{238}}\text{U}$ , first recognized as a new element by the Curies. Poses special problems because its daughter is a radioactive noble gas.

Determine the total force and the absolute pressure on the bottom of a swimming pool 28.0m by 8.5m whose uniform depth is 1 .8m.
for the answer to complete, the units need specified why
That's just how the AP grades. Otherwise, you could be talking about m/s when the answer requires m/s^2. They need to know what you are referring to.
Kyle
Suppose a speck of dust in an electrostatic precipitator has 1.0000×1012 protons in it and has a net charge of –5.00 nC (a very large charge for a small speck). How many electrons does it have?
how would I work this problem
Alexia
how can you have not an integer number of protons? If, on the other hand it supposed to be 1e12, then 1.6e-19C/proton • 1e12 protons=1.6e-7 C is the charge of the protons in the speck, so the difference between this and 5e-9C is made up by electrons
Igor
what is angular velocity
angular velocity can be defined as the rate of change in radian over seconds.
Fidelis
Why does earth exert only a tiny downward pull?
hello
Islam
Why is light bright?
an 8.0 capacitor is connected by to the terminals of 60Hz whoes rms voltage is 150v. a.find the capacity reactance and rms to the circuit
thanks so much. i undersooth well
what is physics
is the study of matter in relation to energy
Kintu
physics can be defined as the natural science that deals with the study of motion through space,time along with its related concepts which are energy and force
Fidelis
a submersible pump is dropped a borehole and hits the level of water at the bottom of the borehole 5 seconds later.determine the level of water in the borehole
what is power?
power P = Work done per second W/ t. It means the more power, the stronger machine
Sphere
e.g. heart Uses 2 W per beat.
Rohit
A spherica, concave shaving mirror has a radius of curvature of 32 cm .what is the magnification of a persons face. when it is 12cm to the left of the vertex of the mirror
did you solve?
Shii
1.75cm
Ridwan
my name is Abu m.konnek I am a student of a electrical engineer and I want you to help me
Abu
the magnification k = f/(f-d) with focus f = R/2 =16 cm; d =12 cm k = 16/4 =4
Sphere
what do we call velocity
Kings
A weather vane is some sort of directional arrow parallel to the ground that may rotate freely in a horizontal plane. A typical weather vane has a large cross-sectional area perpendicular to the direction the arrow is pointing, like a “One Way” street sign. The purpose of the weather vane is to indicate the direction of the wind. As wind blows pa
hi
Godfred
Godfred
If a prism is fully imersed in water then the ray of light will normally dispersed or their is any difference?
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