NCERT Class 11 Physics Solutions: Chapter 2-Unit and Measurement Part 14

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Question: 2.26

It is claimed that two cesium clocks, if allowed to run for 100 years, free from any disturbance, may differ by only about 0.02 s. what does this imply for the accuracy of the standard cesium clock in measuring a time-interval of 1 s?

Answer: 2.26

  • Difference in time of cesium clocks

  • Time required for this difference = 100 years

  • In the cesium clock shows a time difference of 0.02 s.

  • In 1s, the clock will show a time difference of

  • Hence, the accuracy of a standard cesium clock in measuring a time interval of 1 s is

Question: 2.27

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

Answer: 2.27

  • Diameter of sodium atom = Size of sodium atom

  • Radius of sodium atom,

  • Volume of sodium atom,

  • According to the Avogadro hypothesis, one mole of sodium contains atoms and has a mass of 23 g or

Mass of one atom

  • Density of sodium atom,

  • It is given that the density of sodium in crystalline phase is

  • Hence, the density of sodium atom and the density of sodium in its crystalline phase are not in the same order. This is because in solid phase, atoms are closely packed. Thus, the inter-atomic separation is very small in the crystalline phase.

Question: 2.28

The unit of length convenient on the nuclear scale is a Fermi: 1 Nuclear sizes obey roughly the following empirical relation:

Where r is the radius of the nucleus, A its mass number, and is a constant equal to about, 1.2 f. show that the rule implies that nuclear mass density is nearly constant for different nuclei. Estimate the mass density of sodium nucleus. Compare it with the average mass density of a sodium atom obtained in Exercise. 2.27.

Answer: 2.28

  • Radius of nucleus r is given by the relation,

  • Volume of nucleus,

  • Now, the mass of a nuclei M is equal to its mass number i.e.,

amu

Image shows the formula of density

Image Shows the Formula of Density

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  • Density of nucleus,

  • This relation shows that nuclear mass depends only on constant Hence, the nuclear mass densities of all nuclei are nearly the same.

  • Density of sodium nucleus is given by,