Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • NCERT
  • Estimate the average mass density of a sodium atom assuming its size to be about 2.5 Å. Compare it with the mass density of sodium in its crystalline phase : 970 kgm-3. Are the two densities of the same order of magnitude ? If so, why ?

Q 2.27: Estimate the average mass density of a sodium atom assuming its size to be about 2.5 Å. (Use the known values of Avogadro’s number and the atomic mass of sodium). Compare it with the mass density of sodium in its crystalline phase : 970 \ kg\ m^{-3}. Are the two densities of the same order of magnitude? If so, why?

Answers (1)

Estimate the average mass density of a sodium atom, assuming its size to be about 2.5 Å. (Use the known values of Avogadro’s number and the atomic mass of sodium). Compare it with the mass density of sodium in its crystalline phase: Are the two densities of the same order of magnitude? If so, why? Given, Diameter of sodium = 2.5 \AA

Radius, r = 0.5 \times 2.5 Å = 1.25 \times 10^{-10}\ m 

Now, Volume occupied by each atom  V = (4/3)\pi r^3 = (4/3)\times (22/7)\times(1.25\times 10^{-10})^3

= 8.18 \times 10^{-30} m^3

We know that one mole of sodium has 6.023 \times 10^{23} atoms and a mass of  23 \times 10^{-3} kg

\therefore Mass of each Sodium atom = \frac{23\times10^{-3}}{6.023\times10^{23}} kg

\therefore Density  = mass/volume = (\frac{23\times10^{-3}}{6.023\times10^{23}}\ kg )/ (8.18 \times 10^{-30} m^3) = 466.8 \times 10^{1}\ kgm^{-3}

But the mass density of sodium in its crystalline phase =  970 \ kg\ m^{-3}

\therefore The densities are almost of the same order. In the solid phase, atoms are tightly packed and thus interatomic space is very small.

 

Posted by

Safeer PP

View full answer

Crack CUET with india's "Best Teachers"

  • HD Video Lectures
  • Unlimited Mock Tests
  • Faculty Support
cuet_ads

Similar Questions

Trending Articles/News

anam-khan

CBSE Class 12 board exams 2025 to have 50% competency-based questions; no change in 10th
anam-khan

CBSE Class 12 board exams 2024 over; expected result date, trends of last 10 years
anam-khan

CBSE Class 12 accountancy board exam analysis 2024 out; paper rated easy, balanced

Latest Question