# جرم اتمی

(تغییرمسیر از جرم نسبی)
پرش به ناوبری پرش به جستجو
فارسیEnglish

جرم اتمی یا جرم نسبی، جرم یک ذرهٔ اتمی، زیراتمی یا یک مولکول است. یکای جرم اتمی، یک‌دوازدهم جرم ایزوتوپ کربن-۱۲ (مطابق با جرم مطلق ۱٫٫۶۶۰۵۴۰۲*۱۰−۲۷ کیلوگرم) است.

شیمی‌دان‌ها در سده‌های ۱۸ و ۱۹ میلادی موفق شدند به روش تجربی جرم اتم‌های بسیاری از عنصرهای شناخته‌شده تا آن زمان را به‌طور نسبی انداره‌گیری کنند. چنین آزمایش‌هایی نشان داد که برای مثال جرم یک اتم اکسیژن ۱٫۳۳ برابر جرم یک اتم کربن و جرم یک اتم کلسیم ۲٫۵ برابر جرم یک اتم اکسیژن است. استفاده از این نسبت‌ها در محاسبه‌های آزمایشگاهی کاری بسیار دشوار بود. از این رو، شیمی‌دان‌ها ناگزیر شدند جرم خاصی را به یک عنصر معین نسبت دهند و سپس به کمک نسبت‌های اندازه‌گیری شده، جرم عنصرهای دیگر را محاسبه کنند. سرانجام فراوان‌ترین ایزوتوپ کربن یعنی کربن-۱۲ برای این منظور انتخاب شد.

## تاریخچه

نخستین تلاش‌ها برای تعیین جرم اتمی نسبی در دهه‌های آغازین قرن نوزدهم توسط جان دالتون، توماس تامسون و یاکوب برسلیوس انجام شد. در ابتدا جرم اتمی نسبی (وزن اتمی) نسبت به سبک‌ترین عنصر (هیدروژن) با ورن اتمی برابر ۱٫۰۰ در نظر گرفته می‌شد. در دهه ۱۸۲۰، فرضیه پروت بیان نمود که جرم اتمی همه عناصر باید ضریبی از جرم اتمی هیدروژن باشد؛ ولی برسلیوس نشان داد که این فرضیه برای همه عناصر درست نیست (مانند کلر با جرم اتمی نسبی ۳۵٫۵). هرچند که بعداً مشخص شد، این مطلب به دلیل وجود مخلوطی از ایزوتوپ‌های مختلف یک عنصر است و جرم اتمی هر ایزوتوپ، به تنهایی، تقریباً برابر با ضریبی از جرم هیدروژن (با اختلاف نزدیک ۱٪) است.

### یکای واحد

تا دههٔ ۱۹۶۰، فیزیک‌دان‌ها و شیمی‌دان‌ها از دو مقیاس مختلف برای محاسبه جرم اتمی بهره می‌بردند. فیزیک‌دان‌ها جرم اتمی ایزوتوپ اکسیژن-۱۶ را برابر ۱۶ در نظر می‌گرفتند؛ در حالی که شیمی‌دان‌ها این عدد را برای جرم اتمی مخلوط طبیعی ایزوتوپ‌های اکسیژن (که شامل اکسیژن-۱۷ و اکسیژن-۱۸ نیز می‌شود) لحاظ می‌کردند. با تعریف جرم اتمی برپایه ایزوتوپ کربن-۱۲، هم نظر فیزیک‌دان‌ها برای پایه‌گذاری بر یک ایزوتوپ خالص رعایت شد و هم مقدار آن به مقیاس شیمی‌دان‌ها نزدیک بود.

## کاهش جرم در جرم اتمی

جرم اتمی یک ایزوتوپ، اندکی با عدد جرمی آن تفاوت دارد. این تفاوت، در ابتدا مثبت است. یعنی جرم اتمی ایزوتوپ هیدروژن-۱ اندکی از ۱ بیشتر است. سپس کاهش می‌یابد تا آن که در هلیم-۴ به یک کمینه نسبی می‌رسد. پس از آن، مجدداً در لیتیم، بریلیم و بور افزایش می‌یابد. دلیل این افزایش، کاهش انرژی بستگی هسته‌ای در این سه عنصر است و نتیجه آن، عدم تشکیل این عناصر در هم‌جوشی هیدروژن در ستاره‌ها می‌باشد. در کربن-۱۲، مقدار جرم اتمی با عدد جرمی دقیقاً برابر است. پس از آن، نسبت جرم اتمی به عدد جرمی تا آهن-۵۶ کاهش می‌یابد و سپس دوباره افزایش می‌یابد تا آن که در عناصر سنگین، از مقدار واحد بیشتر می‌شود.

در واقع، شکافت هسته‌ای در عناصر سنگین‌تر از زیرکونیم انرژی‌زا و در عناصر سبک‌تر از نیوبیم، انرژی‌گیر است. از سوی دیگر، هم‌جوشی دو اتم از عناصر سبک‌تر از اسکاندیم، انرژی‌زا و هم‌جوشی عناصر سنگین‌تر از کلسیم، انرژی‌گیر است. (به استثنای هلیم که هم‌جوشی دو اتم آن یا یک اتم آن با یک اتم سبک‌تر، نیاز به انرژی دارد و تنها در فرایند آلفای سه‌گانه می‌تواند هم‌جوشی کند و به کربن-۱۲ تبدیل شود)

برای نمونه، نسبت جرم اتمی به عدد جرمی برای چند ایزوتوپ در جدول زیر آورده می‌شود.

ایزوتوپ جرم اتمی نسبت جرم اتمی
به عدد جرمی
هیدروژن-۱ ۱٫۰۰۷۸۲۵ ۱٫۰۰۷۸۲۵
هلیم-۴ ۴٫۰۰۲۶۰۲ ۱٫۰۰۰۶۵۱
کربن-۱۲ ۱۲ ۱
نیتروژن-۱۴ ۱۴٫۰۰۳۰۷۴ ۱٫۰۰۰۲۲۰
اکسیژن-۱۶ ۱۵٫۹۹۴۹۱۵ ۰٫۹۹۹۶۸۲
آهن-۵۶ ۵۵٫۹۳۴۹۳۸ ۰٫۹۹۸۸۳۸
نیکل-۶۲ ۶۱٫۹۲۸۳۴۵ ۰٫۹۹۸۸۴۴
سرب-۲۰۸ ۲۰۷٫۹۷۶۶۵۲ ۰٫۹۹۹۸۸۸
رادیم-۲۲۶ ۲۲۶٫۰۲۵۴۱۰ ۱٫۰۰۰۱۱۲
اورانیم-۲۳۸ ۲۳۸٫۰۵۰۷۸۸ ۱٫۰۰۰۲۱۳

## اندازه‌گیری جرم اتمی

برای اندازه‌گیری جرم اتمی از روش طیف‌سنجی جرمی استفاده می‌شود که شامل جداسازی یون‌های یک یا چند اتمی بر پایهٔ نسبت جرم به بار (m/z) و اندازه‌گیری m/z و فراوانی یون‌ها در فاز گازی است. به عبارت دقیق‌تر طیف‌سنجی جرمی به بررسی نسبت جرم به بار مولکول‌ها با استفاده از میدان‌های الکتریکی و مغناطیسی می‌پردازد.

## جرم مولکولی

به صورت مشابه جرم اتمی، جرم مولکولی نیز قابل محاسبه است. کافی است که ترکیب شیمیایی مولکول شناخته شده‌باشد. سپس با جمع کردن جرم اتمی اجزای تشکیل دهنده آن، جرم مولکولی برای مولکول مورد نظر به دست می‌آید. برای نمونه، متان (با ترکیب شیمیایی CH4) از یک اتم کربن با جرم اتمی ۱۲٫۰۱۱ و چهار اتم هیدروژن با جرم اتمی ۱٫۰۰۸ تشکیل شده‌است؛ بنابراین جرم مولکولی متان برابر است با:

۱۲٫۰۱۱+۴×۱٫۰۰۸=۱۶٫۰۴۵

## تبدیل به یکاهای استاندارد جرم

یکای استاندارد جرم برای اندازه‌گیری مقدار یک ماده در بزرگ‌مقیاس، مول است. مقدار آن برای یک ماده برابر است با جرم تعدادی از اتم‌های آن ماده که برابر با تعداد اتم‌های موجود در ۱۲ گرم ایزوتوپ کربن-۱۲ باشد. این تعداد با عنوان عدد آووگادرو تعریف می‌شود و مقدار آن تقریباً برابر ۱۰۲۳×۶٫۰۲۲ است.

مقدار یک مول از هر ماده تقریباً برابر با جرم اتمی یا جرم مولکولی آن ماده است. رابطه تبدیل بین یکای جرم اتمی و یکای جرم استاندارد (گرم) برای یک اتم به صورت زیر است:

$1\ {\rm {u}}={M_{\rm {u}} \over N_{\rm {A}}}\ ={{1\ {\rm {g/mol}}} \over N_{\rm {A}}}$ که در آن $M_{\rm {u}}$ ثابت جرم مولی و $N_{\rm {A}}$ عدد آووگادرو هستند.

## منابع

1. IUPAC, Compendium of Chemical Terminology, 2nd ed. (the "Gold Book") (1997). Online corrected version:  (2006–) "atomic mass".
2. De Bievre، P.؛ Peiser، H. S. (۱۹۹۲). «'Atomic weight': The name, its history, definition, and units» (PDF). Pure&App. Chem. ۶۴ (۱۰): ۱۵۳۵. doi:10.1351/pac199264101535.
3. وزن اتمی و ترکیب ایزوتوپی برای همه عناصر
4. *Physical and Biophysical Chemistry Division Commission on Molecular Structure and Spectroscopy, Recommendations for nomenclature and symbolism for mass spectroscopy (including an appendix of terms used in vacuum technology). (Recommendations 1991), Pure and Applied Chemistry, 1991, Vol. 63, No. 10, pp. 1541-1566 doi:10.1351/pac199163101541 Stylized lithium-7 atom: 3 protons, 4 neutrons, and 3 electrons (total electrons are ~​14300th of the mass of the nucleus). It has a mass of 7.016 Da. Rare lithium-6 (mass of 6.015 Da) has only 3 neutrons, reducing the atomic weight (average) of lithium to 6.941.

The atomic mass (ma) is the mass of an atom. Its unit is the dalton (symbol: Da, or u) where 1 dalton is defined as ​112 of the mass of a single carbon-12 atom, at rest. The protons and neutrons of the nucleus account for nearly all of the total mass of atoms, with the electrons and nuclear binding energy making minor contributions. Thus, the atomic mass measured in Da has nearly the same value as the mass number.

When divided by daltons (abbr. Da) (also known as unified atomic mass units), to form a pure numeric ratio, the atomic mass of an atom becomes a dimensionless value called the relative isotopic mass (see section below). Thus, the atomic mass of a carbon-12 atom is 12 Da (or 12 u), but the relative isotopic mass of a carbon-12 atom is simply 12.

The atomic mass or relative isotopic mass refers to the mass of a single particle and therefore is tied to a certain specific isotope of an element. The dimensionless standard atomic weight instead refers to the average (mathematical mean) of atomic mass values of a typical naturally-occurring mixture of isotopes for a sample of an element. Atomic mass values are thus commonly reported to many more significant figures than atomic weights. Standard atomic weight is related to atomic mass by the abundance ranking of isotopes for each element. It is usually about the same value as the atomic mass of the most abundant isotope, other than what looks like (but is not actually) a rounding difference.

The atomic mass of atoms, ions, or atomic nuclei is slightly less than the sum of the masses of their constituent protons, neutrons, and electrons, due to binding energy mass loss (as per E = mc2).

## Relative isotopic mass: the same quantity as atomic mass, but with different units

Relative isotopic mass (a property of a single atom) is not to be confused with the averaged quantity atomic weight (see above), that is an average of values for many atoms in a given sample of a chemical element.

Relative isotopic mass is similar to atomic mass and has exactly the same numerical value as atomic mass, whenever atomic mass is expressed in unified atomic mass units. The only difference in that case, is that relative isotopic mass is a pure number with no units. This loss of units results from the use of a scaling ratio with respect to a carbon-12 standard, and the word "relative" in the term "relative isotopic mass" refers to this scaling relative to carbon-12.

The relative isotopic mass, then, is the mass of a given isotope (specifically, any single nuclide), when this value is scaled by the mass of carbon-12, when the latter is set equal to 12. Equivalently, the relative isotopic mass of an isotope or nuclide is the mass of the isotope relative to 1/12 of the mass of a carbon-12 atom.

For example, the relative isotopic mass of a carbon-12 atom is exactly 12. For comparison, the atomic mass of a carbon-12 atom is exactly 12 daltons. Alternately, the atomic mass of a carbon-12 atom may be expressed in any other mass units: for example, the atomic mass of a carbon-12 atom is about 1.998467052×10−26 kg.

As in the case of atomic mass, no nuclides other than carbon-12 have exactly whole-number values of relative isotopic mass. As is the case for the related atomic mass when expressed in daltons, the relative isotopic mass numbers of nuclides other than carbon-12 are not whole numbers, but are always close to whole numbers. This is discussed more fully below.

## Similar terms for different quantities

The atomic mass and relative isotopic mass are sometimes confused, or incorrectly used, as synonyms of relative atomic mass (also known as atomic weight) and the standard atomic weight (a particular variety of atomic weight, in the sense that it is standardized). However, as noted in the introduction, atomic weight and standard atomic weight represent terms for (abundance-weighted) averages of atomic masses in elemental samples, not for single nuclides. As such, atomic weight and standard atomic weight often differ numerically from relative isotopic mass and atomic mass, and they can also have different units than atomic mass when this quantity is not expressed in daltons (see the linked article for atomic weight).

The atomic mass (relative isotopic mass) is defined as the mass of a single atom, which can only be one isotope (nuclide) at a time, and is not an abundance-weighted average, as in the case of relative atomic mass/atomic weight. The atomic mass or relative isotopic mass of each isotope and nuclide of a chemical element is therefore a number that can in principle be measured to a very great precision, since every specimen of such a nuclide is expected to be exactly identical to every other specimen, as all atoms of a given type in the same energy state, and every specimen of a particular nuclide, are expected to be exactly identical in mass to every other specimen of that nuclide. For example, every atom of oxygen-16 is expected to have exactly the same atomic mass (relative isotopic mass) as every other atom of oxygen-16.

In the case of many elements that have one naturally occurring isotope (mononuclidic elements) or one dominant isotope, the actual numerical similarity/difference between the atomic mass of the most common isotope, and the (standard) relative atomic mass or (standard) atomic weight can be small or even nil, and does not affect most bulk calculations. However, such an error can exist and even be important when considering individual atoms for elements that are not mononuclidic.

For non-mononuclidic elements that have more than one common isotope, the numerical difference in relative atomic mass (atomic weight) from even the most common relative isotopic mass, can be half a mass unit or more (e.g. see the case of chlorine where atomic weight and standard atomic weight are about 35.45). The atomic mass (relative isotopic mass) of an uncommon isotope can differ from the relative atomic mass, atomic weight, or standard atomic weight, by several mass units.

Atomic masses expressed in daltons (i.e. relative isotopic masses) are always close to whole-number values, but never (except in the case of carbon-12) exactly a whole number, for two reasons:

• protons and neutrons have different masses, and different nuclides have different ratios of protons and neutrons.
• atomic masses are reduced, to different extents, by their binding energies.

The ratio of atomic mass to mass number (number of nucleons) varies from about 0.99884 for 56Fe to 1.00782505 for 1H.

Any mass defect due to nuclear binding energy is experimentally a small fraction (less than 1%) of the mass of an equal number of free nucleons. When compared to the average mass per nucleon in carbon-12, which is moderately strongly-bound compared with other atoms, the mass defect of binding for most atoms is an even smaller fraction of a dalton (unified atomic mass unit, based on carbon-12). Since free protons and neutrons differ from each other in mass by a small fraction of a dalton (about 0.0014 Da), rounding the relative isotopic mass, or the atomic mass of any given nuclide given in daltons to the nearest whole number always gives the nucleon count, or mass number. Additionally, the neutron count (neutron number) may then be derived by subtracting the number of protons (atomic number) from the mass number (nucleon count).

## Mass defects in atomic masses

The amount that the ratio of atomic masses to mass number deviates from 1 is as follows: the deviation starts positive at hydrogen-1, then decreases until it reaches a local minimum at helium-4. Isotopes of lithium, beryllium, and boron are less strongly bound than helium, as shown by their increasing mass-to-mass number ratios.

At carbon, the ratio of mass (in daltons) to mass number is defined as 1, and after carbon it becomes less than one until a minimum is reached at iron-56 (with only slightly higher values for iron-58 and nickel-62), then increases to positive values in the heavy isotopes, with increasing atomic number. This corresponds to the fact that nuclear fission in an element heavier than zirconium produces energy, and fission in any element lighter than niobium requires energy. On the other hand, nuclear fusion of two atoms of an element lighter than scandium (except for helium) produces energy, whereas fusion in elements heavier than calcium requires energy. The fusion of two atoms of He-4 to give beryllium-8 would require energy, and the beryllium would quickly fall apart again. He-4 can fuse with tritium (H-3) or with He-3, and these processes occurred during Big Bang nucleosynthesis. The formation of elements with more than seven nucleons requires the fusion of three atoms of He-4 in the so-called triple alpha process, skipping over lithium, beryllium, and boron to produce carbon.

Here are some values of the ratio of atomic mass to mass number:

Nuclide Ratio of atomic mass to mass number
1H 1.00782505
2H 1.0070508885
3H 1.0053497592
3He 1.0053431064
4He 1.0006508135
6Li 1.0025204658
12C 1
14N 1.0002195718
16O 0.9996821637
56Fe 0.9988381696
210Po 0.9999184462
232Th 1.0001640315
238U 1.0002133958

## Measurement of atomic masses

Direct comparison and measurement of the masses of atoms is achieved with mass spectrometry.

## Conversion factor between atomic mass units and grams

The standard scientific unit used to quantify the amount of a substance in macroscopic quantities is the mole (symbol: mol), which is defined arbitrarily as the amount of a substance which has as many atoms or molecules as there are atoms in 12 grams of the carbon isotope C-12. The number of atoms in a mole is called the Avogadro number, the value of which is approximately 6.022 × 1023.

One mole of a substance always contains almost exactly the standard atomic weight or molar mass of that substance; however, this may or may not be true for the atomic mass, depending on whether or not the element exists naturally in more than one isotope. For example, the standard atomic weight of iron is 55.847 g/mol, and therefore one mole of iron as commonly found on earth has a mass of 55.847 grams. The atomic mass of the 56Fe isotope is 55.935 Da and one mole of 56Fe atoms would then in theory have a mass of 55.935 g, but such amounts of pure 56Fe have never been found (or separated out) on Earth. However, there are 22 mononuclidic elements of which essentially only a single isotope is found in nature (common examples are fluorine, sodium, aluminum and phosphorus) and for these elements the standard atomic weight and atomic mass are the same. Samples of these elements therefore may serve as reference standards for certain atomic mass values.

The formula used for conversion between atomic mass units and SI mass in grams for a single atom is:

$1\ {\rm {u}}={M_{\rm {u}} \over N_{\rm {A}}}\ ={{1\ {\rm {g/mol}}} \over N_{\rm {A}}}$ where $M_{\rm {u}}$ is the Molar mass constant and $N_{\rm {A}}$ is the Avogadro constant.

## Relationship between atomic and molecular masses

Similar definitions apply to molecules. One can compute the molecular mass of a compound by adding the atomic masses of its constituent atoms (nuclides). One can compute the molar mass of a compound by adding the relative atomic masses of the elements given in the chemical formula. In both cases the multiplicity of the atoms (the number of times it occurs) must be taken into account, usually by multiplication of each unique mass by its multiplicity.

## History

The first scientists to determine relative atomic masses were John Dalton and Thomas Thomson between 1803 and 1805 and Jöns Jakob Berzelius between 1808 and 1826. Relative atomic mass (Atomic weight) was originally defined relative to that of the lightest element, hydrogen, which was taken as 1.00, and in the 1820s, Prout's hypothesis stated that atomic masses of all elements would prove to be exact multiples of that of hydrogen. Berzelius, however, soon proved that this was not even approximately true, and for some elements, such as chlorine, relative atomic mass, at about 35.5, falls almost exactly halfway between two integral multiples of that of hydrogen. Still later, this was shown to be largely due to a mix of isotopes, and that the atomic masses of pure isotopes, or nuclides, are multiples of the hydrogen mass, to within about 1%.

In the 1860s, Stanislao Cannizzaro refined relative atomic masses by applying Avogadro's law (notably at the Karlsruhe Congress of 1860). He formulated a law to determine relative atomic masses of elements: the different quantities of the same element contained in different molecules are all whole multiples of the atomic weight and determined relative atomic masses and molecular masses by comparing the vapor density of a collection of gases with molecules containing one or more of the chemical element in question.

In the 20th century, until the 1960s, chemists and physicists used two different atomic-mass scales. The chemists used a "atomic mass unit" (amu) scale such that the natural mixture of oxygen isotopes had an atomic mass 16, while the physicists assigned the same number 16 to only the atomic mass of the most common oxygen isotope (16O, containing eight protons and eight neutrons). However, because oxygen-17 and oxygen-18 are also present in natural oxygen this led to two different tables of atomic mass. The unified scale based on carbon-12, 12C, met the physicists' need to base the scale on a pure isotope, while being numerically close to the chemists' scale. This was adopted as the 'unified atomic mass unit'. The current International System of Units (SI) primary recommendation for the name of this unit is the dalton and symbol 'Da'. The name 'unified atomic mass unit' and symbol 'u' are recognized names and symbols for the same unit.

The term atomic weight is being phased out slowly and being replaced by relative atomic mass, in most current usage. This shift in nomenclature reaches back to the 1960s and has been the source of much debate in the scientific community, which was triggered by the adoption of the unified atomic mass unit and the realization that weight was in some ways an inappropriate term. The argument for keeping the term "atomic weight" was primarily that it was a well understood term to those in the field, that the term "atomic mass" was already in use (as it is currently defined) and that the term "relative atomic mass" might be easily confused with relative isotopic mass (the mass of a single atom of a given nuclide, expressed dimensionlessly relative to 1/12 of the mass of carbon-12; see section above).

In 1979, as a compromise, the term "relative atomic mass" was introduced as a secondary synonym for atomic weight. Twenty years later the primacy of these synonyms was reversed, and the term "relative atomic mass" is now the preferred term.

However, the term "standard atomic weights" (referring to the standardized expectation atomic weights of differing samples) has not been changed, because simple replacement of "atomic weight" with "relative atomic mass" would have resulted in the term "standard relative atomic mass."