Question

One atom of an element weighs \[3.32\times {{10}^{-23}}g.\] How many grams are there in \[20kg\] of elements?
A) $2000$
B) $20$
C) $200$
D) $1000$

Answer 1

Hint: We know that In order to solve the given problem we will use the basic concept of chemistry that is the mass of a single unit nucleon. Further by the help of the unitary method of problem solving we will find the number of nucleons comprising two atoms by dividing the weight of one atom by the mass of one nucleon and then multiplying it by \[2\] for \[2\] atoms.

Complete answer:
As we know that the number of nucleons comprising an atom is found out by using the mass of one nucleon. Given that the mass of one atom is \[3.32\times {{10}^{-23}}g.\] We know that the nucleon can be either a proton or neutron. We know that the mass of one nucleon is approximately given as: \[1.67\times {{10}^{-24}}g.\] . Now we have the mass of one atom and the mass of one neutron so in order to
Mass of one atom \[=3.32\times {{10}^{-23}}g\] and Mass of $n$ atoms \[=~20kg=20000g\]
Therefore, \[n=\dfrac{20000}{3.32\times {{10}^{-23}}}=6.024\times {{10}^{26~}}atoms.\]
As we know that, \[1\text{ }gram\text{ }atom~=6.023\times {{10}^{23}}~atoms\]
\[\therefore \left[ \left( Number\text{ }of\text{ }gram\text{ }atoms \right)~\times \left( 6.023\times {{10}^{23}} \right) \right]=\left[ 6.024\times {{10}^{26}} \right]~\]
And we know that number of gram atoms \[=1000\]

Thus the correct answer is option ‘D’.

Note: Remember that In order to solve such types of problems students must remember the mass of one nucleon. Also similar types of problems may be asked to find the no of electrons so students must remember the weight of one electron. In the given problem there may be presence of electrons in the same atoms but we have not taken them into account as the weight of electrons is rather negligible as compared to the mass of the nucleon.