Question

If Avogadro's number would have been $1\times {10}^{23}$, instead of $6.02\times {10}^{23}$ then mass of one atom of ${}_8^{16}O$ would be:

• A. $1amu$
• B. $1\times {10}^{10}amu$
• C. $16amu$
• D. $6\times {10}^{13}amu$

Answer 1

Answer: (C)

$16amu$

Atomic weight of $O=16g/mole$

We know that $1$ mole of $O$ contains $N_a=6.023\times {10}^{23}$ number of atoms (Avogadro's Number of atoms)

Therefore, mass of $6.023\times {10}^{23}$ atoms of $O=16g$

$\Rightarrow$ Mass of $1$ atom of $O=\frac{16g}{6.023\times {10}^{23}}....\left(i\right)$

Now, $1amu=\frac{1}{12}th$ the mass of one ${}^{12}C$ atom.

Atomic weight of carbon-12 atom $=12g$

$12g$ of ${}^{12}C$ atom contains $6.023\times {10}^{23}$ atoms.

Therefore, mass of $1$ atom of ${}^{12}C=\frac{12}{6.023\times {10}^{23}}$

$\therefore \frac{1}{12}th$ the mass of $1$ ${}^{12}C$ atom $=1amu=\frac{1}{12}\times \frac{12}{6.023\times {10}^{23}}=\frac{1}{6.023\times {10}^{23}}$

Now, according to the given condition, $N_a=1\times {10}^{23}$ instead of

$6.023\times {10}^{23}$.

So, $1amu$ will now be $=\frac{1}{1\times {10}^{23}}$

Now, putting the value of $1amu$ in equation $\left(i\right)$, we get;

Mass of $1$ atom of $O=\frac{16}{1\times {10}^{23}}g=16\times {10}^{-23}g$

The value of mass of $1$ atom of oxygen in $amu$:

$16\times {10}^{-23}\times \frac{1}{1\times {10}^{23}}amu$

$=16amu$

Hence, option (C) is correct.