GREPhysics.NET: GR8677 #17

GR8677 #17

Problem

GREPhysics.NET Official Solution

Advanced Topics $\Rightarrow$ }Radioactivity

$X^A_Z\rightarrow ? \rightarrow ? \rightarrow Y^{A-4}_{Z-1}$ by natural decay
Recall the following decay processes, and recall that the subscripts and superscripts have to balance on both sides of the arrow.

Beta ( $\beta^-$ ) Decay:

$X^A_Z\rightarrow X'^A_{Z+1} + \beta^0_{-1} +\bar{\nu}, <br />$

where $\bar{\nu}$ is the symbol of an anti-neutrino. (The $\beta^+$ decay is accompanied by a neutrino, $\nu$ , instead of an anti-neutrino.)

Alpha Decay:

$X^A_Z\rightarrow X'^{A-4}_{Z-2}+He^{4}_{2}$

Gamma Decay (no change in A or Z):

$X^A_Z\rightarrow X^A_Z\rightarrow + \gamma <br />$

Deuteron Decay (rare):

$X^A_Z\rightarrow X^{A-2}_{Z-1}+H^2_1<br />$

(A) $X^A_Z\rightarrow X^A_{Z+1} + \beta^0_{-1} \rightarrow X'^{A-4}_{Z-1} +He^4_2 \rightarrow Y^{A-4}_{Z-1}$ . This works out.

(B) $\beta^-$ decay always occurs with an antineutrino.

(C) $\gamma$ emission doesn't change the atomic number.

(D) Although the numbers work out here, deuteron decay is rare, thus not natural.

(E) The subscripts and superscripts don't add up.

Alternate Solutions

There are no Alternate Solutions for this problem. Be the first to post one!

Comments

jmason86
2009-08-12 21:37:41

I believe ETS made a typo in the problem statement. The subscript on Y should be Z+1 to be consistent with the rest of the problem.
That is because if Z (the # of protons) decreases by 1, it implies a proton turning into a neutron ( $\beta^+$ decay). To conserve charge you must emit a positron and to conserve lepton number (from the positron) you must also emit an electron neutrino.

In short, p -> n + e $^+ +\nu_e$

Correct me if I'm wrong :)

segfault
2009-08-22 22:06:46

After the *first* stage in the process the subscript should be Z+1, but after alpha emission the subscript becomes Z+1-2=Z-1. This is a two step process.

Reply to this comment

Post A Comment!

Bare Basic LaTeX Rosetta Stone
LaTeX syntax supported through dollar sign wrappers $, ex., $\alpha^2_0$ produces $\alpha^2_0$ .
type this...	to get...
$\int_0^\infty$	$\int_0^\infty$
$\partial$	$\partial$
$\Rightarrow$	$\Rightarrow$
$\ddot{x},\dot{x}$	$\ddot{x},\dot{x}$
$\sqrt{z}$	$\sqrt{z}$
$\langle my \rangle$	$\langle my \rangle$
$\left( abacadabra \right)_{me}$	$\left( abacadabra \right)_{me}$
$\vec{E}$	$\vec{E}$
$\frac{a}{b}$	$\frac{a}{b}$

The Sidebar Chatbox...
Scroll to see it, or resize your browser to ignore it...

All-Solutions List | Latest Comments | Unanswered Questions (Cries for Help!) |::| About

This site is not affiliated with ETS, nor is it officially endorsed (yet) by ETS. This site is the work of an individual named Yosun Chang. The solutions, sans user comments and ETS questions, are © 2005 by Yosun Chang except where noted. All rights reserved. / The comments appending particular solutions are due to the respective users. / Educational Testing Service, ETS, the ETS logo, Graduate Record Examinations, and GRE are registered trademarks of Educational Testing Service. The examination questions are © 1997 and © 2001 by ETS.

Bare Basic LaTeX Rosetta Stone