Hidden radian units - Revision history

Bugman: Changed the {{warning}} to a {{caution}}.

2015-11-19T14:31:26Z

Changed the {{warning}} to a {{caution}}.

Bugman: Shifted the warning to the start of the article.

2015-11-05T13:15:34Z

Shifted the warning to the start of the article.

Bugman: /* Introduction */ Converted the warning text to use the {{Warning}} template.

2015-10-15T14:46:39Z

Introduction: Converted the warning text to use the {{Warning}} template.

Bugman: Deletion of the tag as the MetaKeywordsTag extension is not installed (https://www.mediawiki.org/wiki/Extension:MetaKeywordsTag).

2015-10-15T14:05:26Z

Deletion of the <keywords> tag as the MetaKeywordsTag extension is not installed (https://www.mediawiki.org/wiki/Extension:MetaKeywordsTag).

Bugman: /* Spherical harmonics */ Fix for the symbols in the text.

2015-09-22T13:53:26Z

Spherical harmonics: Fix for the symbols in the text.

Bugman admin: /* See also */

2013-08-13T09:14:12Z

Bugman admin at 09:11, 13 August 2013

2013-08-13T09:11:19Z

Bugman: /* Introduction */ More editing.

2013-07-24T17:17:48Z

Introduction: More editing.

Bugman: /* Book quotations */ Better formatting throughout.

2013-07-24T17:02:41Z

Book quotations: Better formatting throughout.

Bugman: /* Book quotations */ Better formatting throughout.

2013-07-24T16:57:16Z

Book quotations: Better formatting throughout.

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← Older revision		Revision as of 14:31, 19 November 2015
Line 1:		Line 1:
−	{{~~Warning~~\|If hard core NMR or physics theory is not to your taste, please do not read any further!}}	+	{{Caution\|If hard core NMR or physics theory is not to your taste, please do not read any further!}}

	A major point of confusion in the NMR field is that of the dimensionless and hidden radian unit. This often results in people mistakenly writing Hertz units when inverse seconds (or rad/s) should have been used. This issue can be traced back to the [http://en.wikipedia.org/wiki/International_System_of_Units SI] organisation itself. Specifically the SI supplementary units definitions whereby the assumption is made that if a process is rotational, a physicist should know that radian units are implicit.		A major point of confusion in the NMR field is that of the dimensionless and hidden radian unit. This often results in people mistakenly writing Hertz units when inverse seconds (or rad/s) should have been used. This issue can be traced back to the [http://en.wikipedia.org/wiki/International_System_of_Units SI] organisation itself. Specifically the SI supplementary units definitions whereby the assumption is made that if a process is rotational, a physicist should know that radian units are implicit.

@@ Line 1: / Line 1: @@
 A major point of confusion in the NMR field is that of the dimensionless and hidden radian unit.  This often results in people mistakenly writing Hertz units when inverse seconds (or rad/s) should have been used.  This issue can be traced back to the [http://en.wikipedia.org/wiki/International_System_of_Units SI] organisation itself.  Specifically the SI supplementary units definitions whereby the assumption is made that if a process is rotational, a physicist should know that radian units are implicit.
 == Introduction ==
 The concept of the hidden radian unit is quite important for understanding relaxation in NMR or, in fact, any rotational process in physics.  For example it is important for understanding the model-free equations, for reduced spectral density mapping, for SRLS, and for relaxation dispersion.  In these cases, the reason is because relaxation rates are measured in rad/s.  As described in [[#SI supplementary units]], the radian unit can be dropped because it is plainly obvious that NMR and relaxation is an angular process and hence radian units are implied (if you didn't get that, that was sarcasm).  Hence R2 can be said to be in units of 1/s, but never, ever Hz.  Also note that because of the SI conventions described below, describing the correlation time in s units does not imply that there are no radian units.  But reporting rates as Hz implies no radian units whereas reporting as 1/s instead indicates that radian units are present.

@@ Line 5: / Line 5: @@
 == Introduction ==
-'''Warning:'''  If hard core NMR or physics theory is not to your taste, please do not read any further!
+{{Warning|If hard core NMR or physics theory is not to your taste, please do not read any further!}}
 The concept of the hidden radian unit is quite important for understanding relaxation in NMR or, in fact, any rotational process in physics.  For example it is important for understanding the model-free equations, for reduced spectral density mapping, for SRLS, and for relaxation dispersion.  In these cases, the reason is because relaxation rates are measured in rad/s.  As described in [[#SI supplementary units]], the radian unit can be dropped because it is plainly obvious that NMR and relaxation is an angular process and hence radian units are implied (if you didn't get that, that was sarcasm).  Hence R2 can be said to be in units of 1/s, but never, ever Hz.  Also note that because of the SI conventions described below, describing the correlation time in s units does not imply that there are no radian units.  But reporting rates as Hz implies no radian units whereas reporting as 1/s instead indicates that radian units are present.

← Older revision		Revision as of 14:05, 15 October 2015
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−	~~<keywords content="diffusion rates, dimensionless units, hidden units, radian, relaxation rates, rotational correlation times, SI supplementary units, spherical harmonics" />~~
−
	A major point of confusion in the NMR field is that of the dimensionless and hidden radian unit. This often results in people mistakenly writing Hertz units when inverse seconds (or rad/s) should have been used. This issue can be traced back to the [http://en.wikipedia.org/wiki/International_System_of_Units SI] organisation itself. Specifically the SI supplementary units definitions whereby the assumption is made that if a process is rotational, a physicist should know that radian units are implicit.		A major point of confusion in the NMR field is that of the dimensionless and hidden radian unit. This often results in people mistakenly writing Hertz units when inverse seconds (or rad/s) should have been used. This issue can be traced back to the [http://en.wikipedia.org/wiki/International_System_of_Units SI] organisation itself. Specifically the SI supplementary units definitions whereby the assumption is made that if a process is rotational, a physicist should know that radian units are implicit.

@@ Line 77: / Line 77: @@
 </math>
-where <math alt="theta(t)">\theta(t)</math> and <math alt="phi(t)">\phi(t)</math> are the time dependent spherical angles in the dimensionless radian units.  The time t is normal time and hence has no hidden radian units.  Spherical harmonics are the angular portion of the solution to Laplace's equation and, because it is angular, it is using the radian angular SI unit.
+where ''θ(t)'' and ''ϕ(t)'' are the time dependent spherical angles in the dimensionless radian units.  The time ''t'' is normal time and hence has no hidden radian units.  Spherical harmonics are the angular portion of the solution to Laplace's equation and, because it is angular, it is using the radian angular SI unit.
 == Rotational correlation times ==

← Older revision		Revision as of 09:14, 13 August 2013
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−	== See also ==	+	= See also =

	[[Category:Theory]]		[[Category:Theory]]

← Older revision		Revision as of 09:11, 13 August 2013
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	;Quote (page 37)		;Quote (page 37)
	<blockquote>...T1 relaxation is inversely proportional to correlation time tau_c...</blockquote>		<blockquote>...T1 relaxation is inversely proportional to correlation time tau_c...</blockquote>
		+
		+
		+	== See also ==
		+
		+	[[Category:Theory]]

@@ Line 9: / Line 9: @@
 '''Warning:'''  If hard core NMR or physics theory is not to your taste, please do not read any further!
-This concept is quite important for understanding relaxation in NMR or, in fact, any rotational process in physics.  It is important for understanding the model-free equations, for reduced spectral density mapping, for SRLS, and for relaxation dispersion.  The reason is because relaxation rates are measured in rad/s.  As described in [[#SI supplementary units]], the radian unit can be dropped because it is plainly obvious that NMR and relaxation is an angular process and hence radian units are implied (that was sarcastic).  Hence R2 can be said to be in units of 1/s, but never, ever Hz.  Also note that because of the SI conventions described below, describing the correlation time in s units does not imply that there are no radian units.  But reporting rates as Hz implies no radian units whereas reporting as 1/s instead indicates that radian units are present.
+The concept of the hidden radian unit is quite important for understanding relaxation in NMR or, in fact, any rotational process in physics.  For example it is important for understanding the model-free equations, for reduced spectral density mapping, for SRLS, and for relaxation dispersion.  In these cases, the reason is because relaxation rates are measured in rad/s.  As described in [[#SI supplementary units]], the radian unit can be dropped because it is plainly obvious that NMR and relaxation is an angular process and hence radian units are implied (if you didn't get that, that was sarcasm).  Hence R2 can be said to be in units of 1/s, but never, ever Hz.  Also note that because of the SI conventions described below, describing the correlation time in s units does not imply that there are no radian units.  But reporting rates as Hz implies no radian units whereas reporting as 1/s instead indicates that radian units are present.
 This is also a follow on from the [https://mail.gna.org/public/relax-devel/2007-06/msg00012.html comprehensive unit analysis of Abragam's relaxation equations].
 == Source ==

@@ Line 303: / Line 303: @@
 === Book quotations ===
-Title:  Practical NMR Relaxation for Chemists
+;Title
-Author:  Vladimir I. Bakhmutov
+:Nuclear Spin Relaxation in Liquids: Theory, Experiments, and Applications
-Subject:  NMR relaxation
+;Authors
-Year:  2004
+:Józef Kowalewski, Lena Mäler
-Link:
+;Subject
-http://books.google.com/books?id=_gIh9KHIOx4C&pg=PA13&dq=rotational+correlation+time+radian&lr=
+:NMR relaxation
-Quote (page 9):  "...linewidths, Delta_nu, measured in Hz, are
+;Year
-directly controlled by T1 and T2 relaxation times according to:
+:2006
-   Delta_nu = 1/(pi T1,2)"
+;Link
-Title:  Modern Protein Chemistry: Practical Aspects
+;Title
-Authors:  Gary C. Howard, William E. Brown
+:Practical NMR Relaxation for Chemists
-Subject:  NMR relaxation
+;Author
-Year:  2001
+:Vladimir I. Bakhmutov
-Link:
+;Subject
-http://books.google.com/books?id=MIxdC7GPz0sC&pg=PA45&dq=rotational+correlation+time+radian&lr=
+:NMR relaxation
-Quote (page 45):  "The actual relationship between the spin-spin
+;Year
-relation rate and the lines width (Delta_nu) is given by R2, the rate
+:2004
-of spin-spin relaxation; T2 is the time constant for spin-spin
+;Link
-relaxation,
+: http://books.google.com/books?id=_gIh9KHIOx4C&pg=PA13&dq=rotational+correlation+time+radian&lr=
-   Delta_nu = 1/pi . R2 = 1/(pi.T2)."
+;Quote (page 9)
-Title:  Structural Biology: Practical NMR Applications
+;Title
-Author:  Quincy Teng
+:Modern Protein Chemistry: Practical Aspects
-Subject:  NMR relaxation
+;Authors
-Year:  2005
+:Gary C. Howard, William E. Brown
-Link:
+;Subject
-http://books.google.com/books?id=dRmmGFkummIC&pg=PA36&dq=rotational+correlation+time+radian&lr=#PPA36,M1
+:NMR relaxation
-Quote (page 37):  "...T1 relaxation is inversely proportional to
+;Year
-correlation time tau_c..."
+:2001