States of Matter - Result Question 65
####65. If the value of Avogadro number is $6.023 \times 10^{23} mol^{-1}$ and the value of Boltzmann constant is $1.380 \times 10^{-23} JK^{-1}$, then the number of significant digits in the calculated value of the universal gas constant is
(2014 Adv.)
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Answer:
Correct Answer: 65. (4)
Solution:
- PLAN This problem can be solved by using the concept involved in calculation of significant figure.
Universal gas constant, $R=k N _A$
where, $\quad k=$ Boltzmann constant
and $\quad N _A=$ Avogadro’s number
$$ \begin{aligned} \therefore \quad R & =1.380 \times 10^{-23} \times 6.023 \times 10^{23} J / Kmol \ & =8.31174 \cong 8.312 \end{aligned} $$
Since, $k$ and $N _A$ both have four significant figures, so the value of $R$ is also rounded off upto 4 significant figures.
[When number is rounded off, the number of significant figure is reduced, the last digit is increased by 1 if following digits $\geq 5$ and is left as such if following digits is $\leq 4$.]
Hence, correct integer is (4).
