GREPhysics.NET: GR0177 #68

GR0177 #68

Problem

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Advanced Topics $\Rightarrow$ }Decay

Since Lithium has one less electron than Be, one might think this decay is just $beta$ -decay. However, $beta$ -decay always occurs with a neutrino or anti-neutrino, and since none of the choices show this.

Beta-decay emits either an electron or positron with an antineutrino or neutrino:

$_A^Z N \rightarrow _{A-1}^Z M + \beta^{+} + \nu$

$_A^Z N \rightarrow _{A+1}^Z M + \beta^{-} + \bar{\nu}$

(The bit on antineutrinos and neutrinos has to do with conservation of Electron Lepton number $L_e$ . Namely, electrons and neutrinos have $L_e=1$ , while positrons and antineutrinos have $L_e = -1$ .)

(Also, $\alpha$ -decay emits a Helium atom with 4 neutrons and 2 protons, so the numbers won't work out here.)

The remaining choice is (E). One can check that it's right by noting that it is the only choice that conserves the electron-lepton number.

Alternate Solutions

jmason86
2009-07-14 22:32:55

The quick-thinking, time-pressure solution that I did was:

(A) $alpha$ decay would change the atomic number nucleon number from 7.

$beta$ decay explains the p->n transformation but requires two particles to be emitted (e+/e- and $nu$ / $nu$ bar)
(B) (C) (D) do not satisfy this

Only (E) remains. Electron capture is also basically an odd form of beta decay.. all the particles involved are the same, the equation just changes a bit.

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Comments

jmason86
2009-07-14 22:36:23

Sorry that was sloppy. Here it is again:

The quick-thinking, time-pressure solution that I did was:

(A) $\alpha$ decay would change the nucleon number from 7.

$\beta$ decay explains the p->n transformation but requires two particles to be emitted (e+/e- and $\nu$ / $\nu$ bar)
(B) (C) (D) do not satisfy this

Only (E) remains. Electron capture is also basically an odd form of beta decay.. all the particles involved are the same, the equation just changes a bit.

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jmason86
2009-07-14 22:32:55

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Poop Loops
2008-11-01 20:25:10

I did this by process of elimination since a particle class is only offered spring quarter senior year at my school...

So:

(A) Alpha particle is a helium nucleus. This won't get us anywhere because helium has 2 protons and we are only dropping our Z (number of protons) by one.

(B) This will simply ionize the particle, so it will still be Be, but with a positive charge. No good.

(C) This will lower the mass, but our mass stays constant here. Further, this won't lower the Z number. Nope.

(D) A positron is the anti-particle of the electron. It is exactly like the electron except it has positive charge. You don't get these in run-of-the-mill atoms, so you can throw this away. But, even if you weren't sure, you can still tell that the Z number won't go down because that refers specifically to protons.

(E) Eh? I don't know what this is. Sure, let's go with this. The little bit I do know says that Neutrons are Protons and Electrons combined together, so that helps.

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abby
2007-10-29 10:26:09

isn't an alpha particle a helium atom with 2neutrons and 2protons? why does the answer say 4neutrons.. (typo?)

mrbojeebers
2007-10-29 22:25:21

Appears to be a typo. Perhaps it was meant 4 nucleons. And not to be a stickler over niggling details, but traditionally one denotes the atomic number with letter $Z$ and mass or nucleon number with letter $A$ (i.e. the symbols $A$ and $Z$ are typically swapped in your $\beta$ -decay equations.)

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