Atoms and Atomic Mass Questions in English

(N/A) One atomic mass unit $(amu)$ is a mass unit equal to exactly one-twelfth $(1/12^{th})$ the mass of one atom of carbon-$12$.
The relative atomic masses of all the elements have been determined with respect to an atom of carbon-$12$.

(B) An atom is extremely small in size,making it impossible to see with the naked eye.
Generally,the radius of an atom is on the order of nanometers $(nm)$. For example,the atomic radius of a hydrogen atom is approximately $10^{-10} \, m$ (or $0.1 \, nm$).

(C) One mole of carbon atoms contains $6.022 \times 10^{23}$ atoms (Avogadro's number).
The molar mass of carbon is $12 \, g/mol$.
Therefore,the mass of $6.022 \times 10^{23}$ carbon atoms is $12 \, g$.
The mass of $1$ carbon atom is calculated as:
$\text{Mass of } 1 \text{ atom} = \frac{\text{Molar mass}}{\text{Avogadro's number}}$
$\text{Mass of } 1 \text{ atom} = \frac{12}{6.022 \times 10^{23}} \, g$
$\text{Mass of } 1 \text{ atom} \approx 1.99 \times 10^{-23} \, g$.

(D) The number of atoms in a given mass of an element is calculated using the formula: $\text{Number of atoms} = \frac{\text{Given mass}}{\text{Atomic mass}} \times N_A$,where $N_A$ is Avogadro's number $(6.022 \times 10^{23} \text{ mol}^{-1})$.
For $100\,g$ of Sodium $(Na)$:
$\text{Number of atoms} = \frac{100}{23} \times 6.022 \times 10^{23} \approx 2.618 \times 10^{24}$ atoms.
For $100\,g$ of Iron $(Fe)$:
$\text{Number of atoms} = \frac{100}{56} \times 6.022 \times 10^{23} \approx 1.075 \times 10^{24}$ atoms.
Comparing the two values,$2.618 \times 10^{24} > 1.075 \times 10^{24}$.
Therefore,$100\,g$ of sodium contains a greater number of atoms than $100\,g$ of iron.

(B) The average atomic mass is calculated by taking the weighted average of the isotopic masses based on their percentage abundance.
Given isotopes are $_{35}^{79}Br$ with $49.7\%$ abundance and $_{35}^{81}Br$ with $50.3\%$ abundance.
Average atomic mass $= (79 \times 0.497) + (81 \times 0.503)$
$= 39.263 + 40.743$
$= 80.006\,u$

(B) The statement '$Atoms$ are not able to exist independently' is incorrect. While most atoms are highly reactive and do not exist in a free state, the atoms of noble gases (inert gases) like $Helium$, $Neon$, $Argon$, etc., are chemically inert and exist independently as single atoms.

(D) The chemical symbol for sodium is derived from its Latin name,$Natrium$. Therefore,the correct symbol is $Na$.

(D) The mass of one atom of an element is calculated by dividing its atomic mass by the Avogadro constant $(N_A)$.
The atomic mass of oxygen is $16 \, u$.
The Avogadro constant $(N_A)$ is approximately $6.023 \times 10^{23} \, \text{mol}^{-1}$.
Therefore,the mass of one atom of oxygen $= \frac{\text{Atomic mass}}{N_A} = \frac{16}{6.023 \times 10^{23}} \, g$.

(C) The number of moles is calculated using the formula: $\text{Number of moles} = \frac{\text{Given mass}}{\text{Molar mass}}$.
Given mass of magnesium = $12 \, g$.
Molar mass of magnesium = $24 \, g \, mol^{-1}$.
Therefore,$\text{Number of moles} = \frac{12}{24} = 0.5 \, mol$.

(B) We know that $1 \, mol$ of any substance contains $6.022 \times 10^{23}$ particles (Avogadro's number).
To find the number of moles of oxygen atoms,we use the formula:
$\text{Number of moles} = \frac{\text{Given number of atoms}}{\text{Avogadro's number}}$
$\text{Number of moles} = \frac{2.58 \times 10^{24}}{6.022 \times 10^{23}}$
$\text{Number of moles} = \frac{25.8 \times 10^{23}}{6.022 \times 10^{23}} \approx 4.28 \, mol$
Therefore,the sample contains $4.28 \, mol$ of oxygen atoms.

(A) The mass of sodium atoms taken by Krish $= (5 \times 23) \, g = 115 \, g$.
The mass of carbon atoms taken by Raunak $= (5 \times 12) \, g = 60 \, g$.
Since $115 \, g > 60 \, g$,Krish's container is heavier.
$(b)$ Both containers have the same number of atoms because they contain the same number of moles of atoms ($5 \, mol$ each). The number of atoms is calculated as $n \times N_A$,where $n$ is the number of moles and $N_A$ is Avogadro's constant $(6.022 \times 10^{23} \, mol^{-1})$.

(B) To find the number of moles,we divide the total number of entities by Avogadro's number $(N_A = 6.023 \times 10^{23} \, \text{mol}^{-1})$.
Number of moles of stars $= \frac{10^{22}}{6.023 \times 10^{23}}$
Number of moles of stars $= \frac{1}{6.023 \times 10} \approx 0.0166 \, \text{mol}$.

To convert units to kilograms $(kg)$,we use the following conversion factors:
$1 \,g = 10^{-3} \,kg$
$1 \,mg = 10^{-6} \,kg$
$(a)$ $5.84 \times 10^{-3} \,mg = 5.84 \times 10^{-3} \times 10^{-6} \,kg = 5.84 \times 10^{-9} \,kg$
$(b)$ $58.34 \,g = 58.34 \times 10^{-3} \,kg = 5.834 \times 10^{-2} \,kg$
$(c)$ $0.584 \,g = 0.584 \times 10^{-3} \,kg = 5.84 \times 10^{-4} \,kg$
$(d)$ $5.873 \times 10^{-21} \,g = 5.873 \times 10^{-21} \times 10^{-3} \,kg = 5.873 \times 10^{-24} \,kg$

(A) The molar mass of an aluminium atom is $27 \,g \,mol^{-1}$.
An aluminium atom $(Al)$ loses $3$ electrons to form an aluminium ion $(Al^{3+})$.
For $1 \,mol$ of $Al^{3+}$ ions,$3 \,mol$ of electrons are lost.
The mass of $1 \,mol$ of electrons is calculated by multiplying the mass of one electron by Avogadro's number $(N_A = 6.022 \times 10^{23} \,mol^{-1})$.
Mass of $3 \,mol$ of electrons $= 3 \times (9.1 \times 10^{-28} \,g) \times (6.022 \times 10^{23} \,mol^{-1})$.
$= 27.3 \times 6.022 \times 10^{-5} \,g \,mol^{-1} \approx 164.4 \times 10^{-5} \,g \,mol^{-1} = 0.001644 \,g \,mol^{-1}$.
Since the ion has lost mass (electrons),the aluminium atom is heavier than the aluminium ion by the mass of the lost electrons,which is approximately $0.0016 \,g$.

(N/A) mole is a fundamental unit in chemistry used to quantify the amount of a substance.
One mole of any substance contains exactly $6.022 \times 10^{23}$ elementary entities,such as atoms,molecules,ions,or electrons.
This constant value is known as Avogadro's number $(N_A)$.

(N/A) Avogadro's constant $(N_A)$ is defined as the number of constituent particles (atoms,molecules,or ions) present in one mole of any substance. Its value is approximately $6.022 \times 10^{23} \text{ particles/mol}$.
Relationship to a mole: $A$ mole is a unit that represents a specific quantity of substance. By definition,one mole of any substance contains exactly $6.022 \times 10^{23}$ elementary entities. Therefore,the number of particles in one mole is equal to Avogadro's constant.

(N/A) $(i)$ The body that approves the nomenclature of elements and compounds is the International Union of Pure and Applied Chemistry $(IUPAC)$.
$(ii)$ The symbol of sodium is $Na$ because it is derived from its Latin name,$Natrium$. The symbol $S$ is reserved for sulfur.
$(iii)$ $(a)$ An element that forms a diatomic molecule is Hydrogen $(H_2)$.
$(b)$ An element that forms a tetraatomic molecule is Phosphorus $(P_4)$.

(B) Given mass $(m) = 5.75 \, g$.
Atomic mass of sodium $= 23 \, u$.
Molar mass $(M) = 23 \, g/mol$.
The formula for the number of moles $(n)$ is given by: $n = \frac{m}{M}$.
Substituting the values: $n = \frac{5.75}{23} = 0.25 \, \text{moles}$.
Therefore, the number of moles in $5.75 \, g$ of sodium is $0.25 \, \text{moles}$.

(A) $1$. Calculate the number of atoms in $11.5 \, g$ of $Na$:
- Molar mass of $Na = 23 \, g/mol$.
- Number of moles of $Na = \frac{11.5 \, g}{23 \, g/mol} = 0.5 \, mol$.
- Number of atoms in $Na = 0.5 \times 6.022 \times 10^{23} = 3.011 \times 10^{23}$ atoms.
$2$. Calculate the number of atoms in $15 \, g$ of $Ca$:
- Molar mass of $Ca = 40 \, g/mol$.
- Number of moles of $Ca = \frac{15 \, g}{40 \, g/mol} = 0.375 \, mol$.
- Number of atoms in $Ca = 0.375 \times 6.022 \times 10^{23} = 2.258 \times 10^{23}$ atoms.
$3$. Conclusion:
- Since $3.011 \times 10^{23} > 2.258 \times 10^{23}$,$11.5 \, g$ of sodium contains a greater number of atoms.

(B) The molar mass of an oxygen atom $(O)$ is $16 \text{ g/mol}$.
The formula to calculate mass is: $\text{Mass} = \text{number of moles} \times \text{molar mass}$.
Given that the number of moles is $1 \text{ mol}$,the calculation is:
$\text{Mass} = 1 \text{ mol} \times 16 \text{ g/mol} = 16 \text{ g}$.
Therefore,the mass of one mole of oxygen atoms is $16 \text{ g}$.

(A) $1$. For Calcium $(Ca)$: Atomic mass $= 40 \, g/mol$. Moles $= \frac{120 \, g}{40 \, g/mol} = 3 \, mol$. Number of atoms $= 3 \times 6.022 \times 10^{23} = 18.066 \times 10^{23}$ atoms.
$2$. For Iron $(Fe)$: Atomic mass $= 56 \, g/mol$. Moles $= \frac{120 \, g}{56 \, g/mol} \approx 2.143 \, mol$. Number of atoms $= 2.143 \times 6.022 \times 10^{23} \approx 12.905 \times 10^{23}$ atoms (using precise division $120/56 \approx 2.1428$).
$3$. Comparing the two,Calcium has more atoms.
$4$. Difference $= (18.066 - 12.905) \times 10^{23} = 5.161 \times 10^{23}$ atoms.

(A) The number $6.022 \times 10^{23}$ is known as Avogadro's number or Avogadro's constant.
It represents the number of particles (atoms,molecules,or ions) present in one mole of a substance.

(N/A) $J$öns Jacob Berzelius proposed a system for representing elements using symbols. He suggested that the symbols of elements should be derived from one or two letters of their names,typically taken from their English or Latin names. For example,$H$ for Hydrogen and $Ca$ for Calcium.

(N/A) $(i)$ The international organisation that approves the names of elements is the International Union of Pure and Applied Chemistry $(IUPAC)$.
$(ii)$ The symbol of tungsten is $W$ (derived from its German name,Wolfram).

(N/A) $(i)$ Atomic number: It is defined as the total number of protons present in the nucleus of an atom and is denoted by the symbol $Z$. For example,the atomic number of Carbon $(C)$ is $6$,which means it has $6$ protons in its nucleus.
$(ii)$ Mass number: It is defined as the sum of the total number of protons and neutrons present in the nucleus of an atom. It is denoted by the symbol $A$. For example,a Nitrogen $(N)$ atom has $7$ protons and $7$ neutrons,so its mass number is $7 + 7 = 14$.

(A) The ion $M^{3+}$ is formed by the loss of $3$ electrons from a neutral atom $M$.
Since the ion contains $10$ electrons, the number of electrons in the neutral atom $M$ is $10 + 3 = 13$.
In a neutral atom, the number of electrons is equal to the number of protons, which defines the atomic number.
Therefore, the atomic number of element $M$ is $13$.
The mass number is the sum of the number of protons and neutrons.
Mass number = $\text{Atomic number} + \text{Number of neutrons} = 13 + 14 = 27$.

(N/A) Initially,$1/16$th of the mass of a naturally occurring oxygen atom was chosen as the atomic mass unit because this standard allowed the atomic masses of most elements to be expressed as whole numbers or near-whole numbers,making calculations simpler.

(N/A) The molar mass of hydrogen $(H)$ is $1\,g/mol$.
Given mass of hydrogen $= 1\,g$.
Number of moles $= \frac{\text{Given mass}}{\text{Molar mass}} = \frac{1\,g}{1\,g/mol} = 1\,mol$.
Since $1\,mol$ of any substance contains $6.022 \times 10^{23}$ particles (Avogadro's number),the number of hydrogen atoms in $1\,g$ of hydrogen is $6.022 \times 10^{23}$ atoms.

(N/A) The relative atomic mass of an atom is defined as the average mass of the atom as compared to $1/12$th the mass of one carbon-$12$ atom.
Therefore,saying the relative atomic mass of oxygen is $16$ means that one atom of oxygen is $16$ times heavier than $1/12$th of the mass of a carbon-$12$ atom.

(N/A) $Au$ represents Gold.
$(b)$ $Ag$ represents Silver.
$(c)$ $Hg$ represents Mercury.
$(d)$ $Sn$ represents Tin.

(N/A) $(i)$ $(a)$ One atomic mass unit ($1 \text{ amu}$ or $1 \text{ u}$) is a mass unit equal to exactly $\frac{1}{12}$th the mass of one $C-12$ atom.
$(b)$ The relative atomic mass of an element is defined as the average mass of one atom of the element compared to $\frac{1}{12}$th the mass of one $C-12$ atom.
$(ii)$ Atoms of most elements are highly reactive and cannot exist independently. However,they combine to form molecules and ions. These particles aggregate in large numbers to form matter,which we can see,feel,or touch,thereby confirming the presence of atoms.

(N/A) mole of particles (atoms,ions,or molecules) is defined as the amount of a substance that contains the same number of particles as there are in $12 \ g$ of the $C-12$ isotope.
Experimentally,it has been found that $0.012 \ kg$ of carbon-$12$ contains $6.022 \times 10^{23}$ atoms. This number is called Avogadro's number or Avogadro's constant and is represented by the symbol $N_A$ or $N_0$.
The symbol for the unit of mole is $mol$.
Advantage of the Mole Concept:
The mole concept allows for the convenient selection of a specific number of atoms and molecules by relating them to the mass and volume of a chemical substance,making stoichiometric calculations easier.

(N/A) $(i)$ We know that $1$ mole of atoms contains $6.022 \times 10^{23}$ atoms.
Therefore,$0.02$ moles of carbon atoms $= 6.022 \times 10^{23} \times 0.02 = 1.2044 \times 10^{22}$ atoms.
$(ii)$ We know that the molar mass of carbon is $12 \text{ g/mol}$.
Number of moles $= \frac{\text{Given mass}}{\text{Molar mass}} = \frac{30 \text{ g}}{12 \text{ g/mol}} = 2.5$ moles.
Number of atoms $= 2.5 \times 6.022 \times 10^{23} = 1.5055 \times 10^{24}$ atoms.
$(iii)$ We know that $1$ mole of ions contains $6.022 \times 10^{23}$ ions.
Therefore,$6$ moles of aluminium ions $= 6 \times 6.022 \times 10^{23} = 3.6132 \times 10^{24}$ atoms.

(B) Given mass of carbon $= 60 \text{ g}$.
Gram atomic mass of carbon $(C)$ $= 12 \text{ g/mol}$.
We know that,the number of moles is calculated by the formula:
$\text{Number of moles} = \frac{\text{Given mass (in grams)}}{\text{Gram atomic mass}}$.
Substituting the values:
$\text{Number of moles} = \frac{60 \text{ g}}{12 \text{ g/mol}} = 5 \text{ moles}$.
Therefore,there are $5 \text{ moles}$ in $60 \text{ g}$ of carbon.

(B) $(i)$ The atomic mass of carbon is $12 \text{ g/mol}$.
$(ii)$ The number of moles in $60 \text{ g}$ of carbon is calculated as: $\text{Moles} = \frac{\text{Given mass}}{\text{Molar mass}} = \frac{60}{12} = 5 \text{ moles}$.
$(iii)$ The number of atoms is calculated by multiplying the number of moles by Avogadro's number $(N_A = 6.022 \times 10^{23} \text{ atoms/mol})$:
$\text{Number of atoms} = 5 \times 6.022 \times 10^{23} = 3.011 \times 10^{24} \text{ atoms}$.

(A) The number of atoms in a substance is calculated by multiplying the number of moles by Avogadro's constant $(N_A = 6.022 \times 10^{23} \text{ atoms/mol})$.
Number of atoms $= \text{Number of moles} \times N_A$
Number of atoms $= 0.02 \times 6.022 \times 10^{23}$
Number of atoms $= 1.2044 \times 10^{22} \text{ atoms}$.

(N/A) We know that the gram atomic mass of carbon is $12 \text{ g}$.
Further,the mass of $1$ carbon atom is calculated as:
$\text{Mass of 1 atom} = \frac{\text{Gram atomic mass}}{\text{Avogadro's number}} = \frac{12 \text{ g}}{6.022 \times 10^{23}}$
$= 1.99 \times 10^{-23} \text{ g}$
Therefore,the mass of $10$ carbon atoms is:
$= 10 \times 1.99 \times 10^{-23} \text{ g}$
$= 1.99 \times 10^{-22} \text{ g}$

(A) Step $1$: Calculate the number of moles in $16\, g$ of sulphur.
Atomic mass of sulphur $(S)$ = $32\, g/mol$.
Moles of $S = \frac{\text{Given mass}}{\text{Atomic mass}} = \frac{16\, g}{32\, g/mol} = 0.5\, mol$.
Step $2$: Determine the number of atoms.
Since $1\, mol$ of any element contains $6.022 \times 10^{23}$ atoms (Avogadro's number),$0.5\, mol$ of $S$ contains $0.5 \times 6.022 \times 10^{23} = 3.011 \times 10^{23}$ atoms.
Step $3$: Calculate the mass of sodium $(Na)$ containing the same number of atoms.
Atomic mass of sodium $(Na)$ = $23\, g/mol$.
To have the same number of atoms $(3.011 \times 10^{23})$,we need $0.5\, mol$ of sodium.
Mass of $Na = \text{Moles} \times \text{Atomic mass} = 0.5\, mol \times 23\, g/mol = 11.5\, g$.
Therefore,$11.5\, g$ of sodium contains the same number of atoms as $16\, g$ of sulphur.

(C) The molar mass of oxygen atoms $(O)$ is $16 \, g/mol$.
By definition,$1 \, mole$ of any substance contains $6.022 \times 10^{23}$ particles (Avogadro's number).
Therefore,the mass of $6.022 \times 10^{23}$ atoms of oxygen is $16 \, g$.
The mass of one atom of oxygen is calculated by dividing the molar mass by Avogadro's number:
$\text{Mass of one atom} = \frac{\text{Molar mass}}{\text{Avogadro's number}} = \frac{16}{6.023 \times 10^{23}} \, g$.

(B) Dalton's atomic theory stated that atoms are indivisible particles. However,later scientific discoveries revealed that atoms are composed of subatomic particles such as protons,neutrons,and electrons,which means they are divisible. Additionally,the existence of isotopes challenges the postulate that atoms of the same element are identical in mass,as isotopes have the same atomic number but different mass numbers. Among the given options,the concept of indivisibility (Option $B$) and the concept of identical mass (Option $C$) were challenged. However,the most fundamental challenge to the 'indivisibility' of the atom is widely cited as the primary limitation of Dalton's theory.

(D) The atomic mass unit $(u)$ is defined as a mass unit equal to exactly one-twelfth $(1/12)$ of the mass of one carbon-$12$ atom.
This standard was adopted by the $IUPAC$ to provide a consistent reference for measuring the masses of atoms.
Therefore,$1 \, u = (1/12) \times \text{mass of one } C-12 \text{ atom}$.

(D) The mass of an atom or a molecule is extremely small. To express these masses conveniently,a standard unit is required.
Historically,the 'atomic mass unit' $(amu)$ was used,which is now represented by the unified mass unit $(u)$.
This unit is defined as exactly $1/12$th of the mass of one carbon-$12$ atom.
Therefore,the accepted unit for measuring the mass of an atom and a molecule is the atomic mass unit ($amu$ or $u$).

(A) The chemical symbol for sodium is derived from its Latin name,$Natrium$.
Therefore,the correct symbol is $Na$.

(C) The correct answer is $C$.
$1$. Atoms are the building blocks of matter,forming molecules and ions.
$2$. While most atoms are highly reactive and do not exist independently,noble gases (like $He$,$Ne$,$Ar$) exist as independent atoms. Therefore,the statement that 'Atoms are not able to exist independently' is not universally true.
$3$. Atoms are electrically neutral because the number of protons equals the number of electrons.
$4$. Atoms combine in large numbers to form visible matter.

(B) The statement is False.
Explanation: $A$ mole of any substance is defined as the amount of substance that contains exactly $6.02214076 \times 10^{23}$ elementary entities (atoms,molecules,or ions). This constant is known as Avogadro's number $(N_A)$. The value provided in the statement,$6.023 \times 10^{22}$,is incorrect by a factor of $10$.

(N/A) Atomic mass: The atomic mass of an atom is defined as the mass equal to one-twelfth $(1/12)$ of the mass of one atom of carbon-$12$.
Mass number: The mass number is the sum of the total number of protons and neutrons present in the nucleus of an atom.

(N/A) Chlorine exists in nature as two isotopes with atomic masses $35\, u$ and $37\, u$ in the ratio of $3:1$.
Therefore,the average atomic mass of chlorine is calculated as:
$\text{Average Atomic Mass} = (35 \times \frac{3}{4}) + (37 \times \frac{1}{4}) = 26.25 + 9.25 = 35.5\, u$.
This does not imply that any individual chlorine atom has a fractional mass of $35.5\, u$. It indicates that in any natural sample of chlorine,both isotopes are present,and the weighted average mass of these atoms is $35.5\, u$.

(TRUE) The statement is True.
Atomic radius is extremely small and is typically measured in nanometres $(nm)$.
By definition,$1 \, m = 10^9 \, nm$ (or $1 \, nm = 10^{-9} \, m$).

(FALSE) The statement is False.
According to Dalton's Atomic Theory,atoms of a given element are identical in both mass and chemical properties.
Furthermore,the existence of isotopes (atoms of the same element with different masses but identical chemical properties) contradicts the claim that they differ in chemical properties.

(TRUE) The statement is True.
By definition,one atomic mass unit ($amu$ or $u$) is defined as a mass exactly equal to one-twelfth $(1/12)$ of the mass of one carbon-$12$ atom.