Question

One atom of an element X weighs ${ 6.644\times 10 }^{ -23 }$. Calculate the number of gram atoms in 40kg of it.
(A) ${ 10 }^{ 2 }$
(B) ${ 10 }^{ 3 }$
(C) ${ 10 }^{ -2 }$
(D) ${ 10 }^{ 4 }$

Answer 1

Hint: Gram atomic mass: It is defined as the mass, in grams, of one mole of molecules in a monatomic substance component. It is mathematically equivalent to the relative atomic mass (or nuclear weight) in grams.

Complete step-by-step answer:
It is given that,
Weight of one atom = ${ 6.644\times 10 }^{ -23 }$
Weight = ${ 40kg }$ = ${ 40,000g }$
As we know,
1 gram atom = number of atoms in one mole = ${ 6.022\times 10 }^{ 23 }$
So, the gram atomic mass = mass of 1 mole mass of one atom
                                          = ${ 6.644\times 10 }^{ -23 }{ \times }{ 6.022\times 10 }^{ 23 }$
                                           = ${ 40.01g }$
Gram atoms = number of moles = $\frac { mass }{ molar\quad mass } $
So, the number of atoms in 40kg = $\frac { 40000 }{ 40 } $
                                                      = ${ 1000 }$ gram atoms
Therefore, the number of gram atoms in ${ 40kg }$ is ${ 1000 }$ gram atoms.

Hence, the correct option is B.

Additional Information:
Avogadro found that one gram atom of any element contains the same number of atoms and one gram molecule of any substance contains the same number of molecules which is equal to ${ 6.022\times 10 }^{ 23 }$.
This number is called Avogadro's number or constant and the amount of the substance containing ${ 6.022\times 10 }^{ 23 }$ Atoms or molecules is called a mole. Mole is the counting unit in chemistry as it is used to express a large number of atoms or molecules.
Gram atomic mass is only the sub-atomic mass of a substance communicated in grams.

Note: The possibility to make a mistake is in the calculation part. The weight of an atom is given in kilograms, so you have to convert it in grams before substitution.