Question

What ­if you were offered $1 million to count from 1 to $\mathbf{6}\mathbf{\times }{\mathbf{10}}^{\mathbf{23}}$ at a rate of one number each second? Determine your hourly wage. Would you do it? Could you do it?

Short answer

As the mass of carbon- 12 is 6g i.e.,the hourly wages is 6g.

Step-by-step solution

Definition of mole

A mole is a sample of a natural element with a mass equal to the element's atomic mass expressed in grams and contains 1 mole of atoms. This number of atoms is called Avogadro's number.

Calculation of Avogadro’s number

WhenAvogadro's number is, mass of$3.01\times {10}^{23}$atoms of carbon-12 (atomic mass of 12 u) should be 12g.

$\left(3.01\times {10}^{23}\mathrm{atoms}\right)\left(\frac{12\mathrm{u}}{\mathrm{atoms}}\right)=12\mathrm{g}$.

Now,

$3.01\times {10}^{23}$u=1g

Calculation of Avogadro’s number

If Avogadro’s number is $3,01\times {10}^{23}$ it is not considered on the basic of the mole, mass of $3.01\times {10}^{23}$atoms of carbon-12 (atomic mass of 12 u) will be calculated as shown below:

$$\begin{gathered} \left(6.02\times {10}^{23}\mathrm{atoms}\right)\left(\frac{12\mathrm{u}}{\mathrm{atom}}\right)=12\mathrm{g} \\ \mathrm{mass}\mathrm{of}3.01\times {10}^{23}\mathrm{atoms}=\left(\frac{12\mathrm{g}}{\left(6.02\times {10}^{23}\mathrm{atoms}\right)}\right)\left(3.01\times {10}^{23}\right) \end{gathered}$$

$\mathrm{mass}\mathrm{of}3.01\times {10}^{23}\mathrm{atoms}=6\mathrm{g}$

Conclusion

As the mass of carbon- 12 is 6g,the hourly wage is 6g.