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Q)

If $\large\frac{1}{6}$, in place of $\large\frac{1}{12}$ mass of carbon atom is taken to be the relative atomic mass unit, the mass of one mole of a substance will :

$(a)\;Decrease\;twice\\(b)\;Increase\;two\;folds\\(c)\;Remain\;unchanged\\(d)\;Be \;a\;function\;of\;the\;molecular\;mass\;of\;the\;element$

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A)
Step 1:
$N$ depends upon the basis of the atomic weight scale.
$12g$ carbon=$6.023\times 10^{23}$atoms
$1g$ carbon=$\large\frac{6.023\times 10^{23}}{12}$
$6g$ carbon=$\large\frac{6.023\times 10^{23}}{12}$$\times 6 =\large\frac{1}{2} N_A$
We know, $1amu=\large\frac{1}{N}$
$= \large\frac{2}{6.023\times 10^{23}}$
$= 3.3\times 10^{-24}g$
Step 2:
Let, molar mass of an element be M amu
Then, $M\;amu=M\times 3.3\times 10^{-24}g$
$\therefore$ mass of 1 mole =$M\times 3.3\times 10^{-24}$
Av.No=$M\times 3.3\times 10^{-24}\times \large\frac{1}{2}$$\times 6.023\times 10^{23} = Mg$
Hence (c) is the correct answer.
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