# 31.4 Nuclear decay and conservation laws  (Page 6/25)

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## Gamma decay

Gamma decay is the simplest form of nuclear decay—it is the emission of energetic photons by nuclei left in an excited state by some earlier process. Protons and neutrons in an excited nucleus are in higher orbitals, and they fall to lower levels by photon emission (analogous to electrons in excited atoms). Nuclear excited states have lifetimes typically of only about ${\text{10}}^{-\text{14}}$ s, an indication of the great strength of the forces pulling the nucleons to lower states. The $\gamma$ decay equation is simply

${}_{Z}^{A}{\text{X}}_{N}^{*}\to {}_{Z}{}^{A}\text{}{\text{X}}_{N}+{\gamma }_{1}+{\gamma }_{2}+\cdots \phantom{\rule{0.25em}{0ex}}\left(\gamma \phantom{\rule{0.25em}{0ex}}\text{decay}\right)$

where the asterisk indicates the nucleus is in an excited state. There may be one or more $\gamma$ s emitted, depending on how the nuclide de-excites. In radioactive decay, $\gamma$ emission is common and is preceded by $\gamma$ or $\beta$ decay. For example, when ${}^{\text{60}}\text{Co}$ ${\beta }^{-}$ decays, it most often leaves the daughter nucleus in an excited state, written ${}^{\text{60}}\text{Ni*}$ . Then the nickel nucleus quickly $\gamma$ decays by the emission of two penetrating $\gamma$ s:

${}^{\text{60}}\text{Ni*}\to {}^{\text{60}}\text{Ni}+{\gamma }_{1}+{\gamma }_{2}.$

These are called cobalt $\gamma$ rays, although they come from nickel—they are used for cancer therapy, for example. It is again constructive to verify the conservation laws for gamma decay. Finally, since $\gamma$ decay does not change the nuclide to another species, it is not prominently featured in charts of decay series, such as that in [link] .

There are other types of nuclear decay, but they occur less commonly than $\alpha$ , $\beta$ , and $\gamma$ decay. Spontaneous fission is the most important of the other forms of nuclear decay because of its applications in nuclear power and weapons. It is covered in the next chapter.

## 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?

#### Questions & Answers

How is the de Broglie wavelength of electrons related to the quantization of their orbits in atoms and molecules?
How do you convert 0.0045kgcmÂ³ to the si unit?
how many state of matter do we really have like I mean... is there any newly discovered state of matter?
I only know 5: •Solids •Liquids •Gases •Plasma •Bose-Einstein condensate
Thapelo
Alright Thank you
Falana
Which one is the Bose-Einstein
James
can you explain what plasma and the I her one you mentioned
Olatunde
u can say sun or stars are just the state of plasma
Mohit
but the are more than seven
Issa
what the meaning of continuum
What state of matter is fire
fire is not in any state of matter...fire is rather a form of energy produced from an oxidising reaction.
Xenda
Isn`t fire the plasma state of matter?
Walter
all this while I taught it was plasma
Victor
How can you define time?
Time can be defined as a continuous , dynamic , irreversible , unpredictable quantity .
Tanaya
unpredictable? but I can say after one o'clock its going to be two o'clock predictably!
Victor
how can we define vector
mahmud
I would define it as having a magnitude (size)with a direction. An example I can think of is a car traveling at 50m/s (magnitude) going North (direction)
Hanzo
what is the relativity of physics
How do you convert 0.0045kgcm³ to the si unit?
flint
What is the formula for motion
V=u+at V²=u²-2as
flint
S=ut+½at
flint
they are eqns of linear motion
King
S=Vt
Thapelo
v=u+at s=ut+at^\2 v^=u^+2as where ^=2
King
hi
hello
King
Explain dopplers effect
Not yet learnt
Bob
Explain motion with types
Bob
Acceleration is the change in velocity over time. Given this information, is acceleration a vector or a scalar quantity? Explain.
Scalar quantity Because acceleration has only magnitude
Bob
acleration is vectr quatity it is found in a spefied direction and it is product of displcemnt
bhat
its a scalar quantity
Paul
velocity is speed and direction. since velocity is a part of acceleration that makes acceleration a vector quantity. an example of this is centripetal acceleration. when you're moving in a circular patter at a constant speed, you are still accelerating because your direction is constantly changing.
Josh
acceleration is a vector quantity. As explained by Josh Thompson, even in circular motion, bodies undergoing circular motion only accelerate because on the constantly changing direction of their constant speed. also retardation and acceleration are differentiated by virtue of their direction in
fitzgerald
respect to prevailing force
fitzgerald
What is the difference between impulse and momentum?
Manyo
Momentum is the product of the mass of a body and the change in velocity of its motion. ie P=m(v-u)/t (SI unit is kgm/s). it is literally the impact of collision from a moving body. While Impulse is the product of momentum and time. I = Pt (SI unit is kgm) or it is literally the change in momentum
fitzgerald
Or I = m(v-u)
fitzgerald
the tendency of a body to maintain it's inertia motion is called momentum( I believe you know what inertia means) so for a body to be in momentum it will be really hard to stop such body or object..... this is where impulse comes in.. the force applied to stop the momentum of such body is impulse..
Pelumi
Calculation of kinetic and potential energy
K.e=mv² P.e=mgh
Malia
K is actually 1/2 mv^2
Josh
what impulse is given to an a-particle of mass 6.7*10^-27 kg if it is ejected from a stationary nucleus at a speed of 3.2*10^-6ms²? what average force is needed if it is ejected in approximately 10^-8 s?
John
speed=velocity÷time velocity=speed×time=3.2×10^-6×10^-8=32×10^-14m/s impulse [I]=∆momentum[P]=mass×velocity=6.7×10^-27×32×10^-14=214.4×10^-41kg/ms force=impulse÷time=214.4×10^-41÷10^-8=214.4×10^-33N. dats how I solved it.if wrong pls correct me.
Melody
what is sound wave
sound wave is a mechanical longitudinal wave that transfers energy from one point to another
Ogor
its a longitudnal wave which is associted wth compresion nad rearfractions
bhat
what is power
it's also a capability to do something or act in a particular way.
Kayode
Newton laws of motion
Mike
power also known as the rate of ability to do work
Slim
power means capabilty to do work p=w/t its unit is watt or j/s it also represents how much work is done fr evry second
bhat
what does fluorine do?
strengthen and whiten teeth.
Gia
a simple pendulum make 50 oscillation in 1minute, what is it period of oscillation?
length of pendulm?
bhat By By By David Martin By By    By  By By Rhodes