Question

How many years would it take to spend Avogadro's number of rupees at the rate of 1 million rupees in one second?
A. \[19.098 \times {10^{19}}years\]
B. \[19.098{\text{ }}years\]
C. \[19.098 \times {10^9}years\]
D. None of the above.

Answer 1

Hint: The number of units of any material in one mole is called the amount of Avogadro, or the constant of Avogadro. This is the equivalent of \[6.022140857 \times {10^{23}}\]. Depending on the character of the reaction and the existence of the product, the units can be electrons, ions, atoms or molecules.

Complete step-by-step answer:.
Rate of sending rupee = 1million/sec.
\[ = 1 \times {10^6}/\sec \]
\[{\text{Total time = }}\dfrac{{6.022 \times {{10}^{23}}}}{{1 \times {{10}^6}}}{\text{ second}}\]
\[ = 6.022 \times {10^{17}}{\text{ sec = }}\dfrac{{6.022 \times {{10}^{17}}}}{{3600 \times 24 \times 365}}{\text{ years}}\]
= \[19.098 \times {10^9}years\]
Hence, the option C is the right answer.

Note: The Significance of Avogadro’s number:
Substances at the atomic level are measured as per unit of atomic mass. The Atomic mass unit is defined as the weight of 1/12 of one carbon atom's mass.
For instance, Hydrogen's atomic mass unit is 1.00794 amu. Currently it is not possible to quantify the power to tell of a single particle (atom, electron, molecule), to conduct a reaction.
So, chemists then came up with a way of connecting the unit of atomic mass and the gram.
\[1{\text{ amu = 1}}{\text{.66}} \times {\text{1}}{{\text{0}}^{ - 24}}{\text{ grams}}\]
With this, we can differentiate between measurement in grams and the measuring unit of the atomic mass unit that is invisible. And thus, this is the importance of the amount of Avogadro.