The radius of atom is of the order of 1 Å and radius of nucleus is of the order of fermi. How many magnitudes higher is the volume of atom as compared to the volume of nucleus? - Physics

Advertisements
Advertisements
Short Note

The radius of atom is of the order of 1 Å and the radius of nucleus is of the order of fermi. How many magnitudes higher is the volume of atom as compared to the volume of nucleus?

Advertisements

Solution

Radius of atom = 1 Å = 10–10 m

Radius of nucleus = 1 fermi = 1015 m

Volume of atom = VA = `4/3 πR_A^3`

Volume of atom = `4/3 πR_A^3`

Volume of nucleus VN = `4/3 πR_N^3`

`V_A/V_N = (4/3  πR_A^3)/(4/3  πR_N^3)`

= `(R_A/R_N)^3`

= `(10^-10/10^-15)^3`

= 1015

  Is there an error in this question or solution?
Chapter 2: Units and Measurements - Exercises [Page 8]

APPEARS IN

NCERT Exemplar Physics Class 11
Chapter 2 Units and Measurements
Exercises | Q 2.20 | Page 8

RELATED QUESTIONS

The farthest objects in our Universe discovered by modern astronomers are so distant that light emitted by them takes billions of years to reach the Earth. These objects (known as quasars) have many puzzling features, which have not yet been satisfactorily explained. What is the distance in km of a quasar from which light takes 3.0 billion years to reach us?


The nearest star to our solar system is 4.29 light years away. How much is this distance in terms of parsecs? How much parallax would this star (named Alpha Centauri) show when viewed from two locations of the Earth six months apart in its orbit around the Sun?


When the planet Jupiter is at a distance of 824.7 million kilometres from the Earth, its angular diameter is measured to be 35.72″ of arc. Calculate the diameter of Jupiter


Just as precise measurements are necessary in science, it is equally important to be able to make rough estimates of quantities using rudimentary ideas and common observations. Think of ways by which you can estimate the following (where an estimate is difficult to obtain, try to get an upper bound on the quantity):

 

the number of strands of hair on your head


Write true or false.

Every measurement involves two things – a number and a unit.


What are the S.I. units of

  1.  mass
  2.  length
  3.  time and
  4.  temperature.

Write their names and symbols.


Match the following.

 Column A   Column B
(1) Length  a. kilogram
(2) Mass  b. cubic metre
(3) Area  c. metre
(4) Volume  d. square metre

Fill in the blank.

In the ............ system, length is measured in centimetres.


Exercise


Answer the following question.

Star A is farther than star B. Which star will have a large parallax angle?


Solve the numerical example.

When the planet Jupiter is at a distance of 824.7 million kilometers from the Earth, its angular diameter is measured to be 35.72'' of arc. Calculate the diameter of Jupiter.


While measuring the length of an object using a ruler, the position of your eye should be


Ten millimetre makes one centimetre.


A hand span is a reliable measure of length.


Complete the analogy.

Height of a person: cm:: Length of your sharpened pencil lead:___?


Fill in the following chart.

Property Definition Basic Unit Instrument used for measuring
Length      
Mass      
Volume      
Time      

Rulers, measuring tapes and metre scales are used to measure ______


Metre is the unit of ______.


Assertion (A): Distance between two celestial bodies is measured in terms of light year.

Reason (R): The distance travelled by the light in one year is one light year.


Can you find the diameter of a thin wire of length 2 m using the ruler from your instrument box?


Numerical Problem.

Inian and Ezhilan argue about the light year. Inian tells that it is 9.46 × 1015 m and Ezhilan argues that it is 9.46 × 10 12 km. Who is right? Justify your answer.


Have you seen frogs? Where? How many different types of frogs have you seen? Are all the frogs of the same length? Here are two interesting examples.


Which line is longer? C or D? Measure each line. How good is your guess?


Now guess the length and width of many other things. Measure and find the difference between your measure and your guess.

Size of Your guess in cm Your measure in cm
  Length Width Length Width
100 Rupee note        
10 Rupee note        
20 Rupee note        
5 Rupee note        
Post card        
Math-Magic book        

Difference in size
Do this for yourself and find the difference.


How many stamps can be placed along its length?


How many stamps are needed to cover the rectangle?


Arbaz plans to tile his kitchen floor with green square tiles. Each side of the tile is 10 cm. His kitchen is 220 cm in length and 180 cm wide. How many tiles will he need?


Now cut strips of equal sizes out of it. Using tape join the strips, end to end, to make a belt.

How long is your belt? _________


You can play this game on the ground. Make two squares of one square meter each. Divide your class into two teams. Ready to play!

  • Which team could make more children stand in their square? How many?

You can play this game on the ground. Make two squares of one square meter each. Divide your class into two teams. Ready to play!

  • Which team could make more children sit in their square? How many?

There are two beautiful lakes near a village. People come for boating and picnics in both the lakes. The village Panchayat is worried that with the noise of the boats the birds will stop coming. The Panchayat wants motorboats in only one lake. The other lake will be saved for the birds to make their nests.

  • How many cm is the length of the boundary of lake A in the drawing?(use thread to find out)

So Anar also tried many different ways to make a boundary for 800 square meters of land.

He made rectangles A, B, and C of different sizes. Find out the length of the boundary of each. How much gold wire will he get for these rectangles?


  • Gold wire for A = _________ metres

  • Gold wire for B = _________ metres
  • C  
    Gold wire for C = __________ metres

But then Anar made an even longer rectangle... See how long!


  • So he will get __________ metres of gold wire!!

There are two beautiful lakes near a village. People come for boating and picnics in both the lakes. The village Panchayat is worried that with the noise of the boats the birds will stop coming. The Panchayat wants motorboats in only one lake. The other lake will be saved for the birds to make their nests.

  • How many kilometers long is the actual boundary of lake A?

There are two beautiful lakes near a village. People come for boating and picnics in both the lakes. The village Panchayat is worried that with the noise of the boats the birds will stop coming. The Panchayat wants motorboats in only one lake. The other lake will be saved for the birds to make their nests.

  • How many kilometers long is the actual boundary of lake B?

There are two beautiful lakes near a village. People come for boating and picnics in both the lakes. The village Panchayat is worried that with the noise of the boats the birds will stop coming. The Panchayat wants motorboats in only one lake. The other lake will be saved for the birds to make their nests.

  • Find the area of lake B on the drawing in square cm. What is its actual area in square km?

There are two beautiful lakes near a village. People come for boating and picnics in both the lakes. The village Panchayat is worried that with the noise of the boats the birds will stop coming. The Panchayat wants motorboats in only one lake. The other lake will be saved for the birds to make their nests.

  • A longer boundary around the lake will help more birds to lay their eggs. So which lake should be kept for birds? Which lake should be used for boats?

Length is a fundamental quantity.


What formula is used to measure the area of your classroom?


Match the following:

  Prefix   Symbol
a. Centi i. k
b. Nano ii. c
c. Mili iii. n
d. Kilo iv. m

What is the unit of measurements of very small lengths?


What is the unit of length?


Length is ______.


The Unit used to measure length ______.


What unit will you use to measure the length of our classroom?


Yard was used as the unit of length.


The SI unit of mass is kg.


To measure the distance of a planet from the earth, ______ method is used.


  1. The earth-moon distance is about 60 earth radius. What will be the diameter of the earth (approximately in degrees) as seen from the moon?
  2. Moon is seen to be of (½)°diameter from the earth. What must be the relative size compared to the earth?
  3. From parallax measurement, the sun is found to be at a distance of about 400 times the earth-moon distance. Estimate the ratio of sun-earth diameters.

The distance of a galaxy is of the order of 1025 m. Calculate the order of magnitude of time taken by light to reach us from the galaxy.


In an experiment to estimate the size of a molecule of oleic acid 1 mL of oleic acid is dissolved in 19 mL of alcohol. Then 1 mL of this solution is diluted to 20 mL by adding alcohol. Now 1 drop of this diluted solution is placed on water in a shallow trough. The solution spreads over the surface of water forming one molecule thick layer. Now, lycopodium powder is sprinkled evenly over the film and its diameter is measured. Knowing the volume of the drop and area of the film we can calculate the thickness of the film which will give us the size of oleic acid molecule.

Read the passage carefully and answer the following questions:

  1. Why do we dissolve oleic acid in alcohol?
  2. What is the role of lycopodium powder?
  3. What would be the volume of oleic acid in each mL of solution prepared?
  4. How will you calculate the volume of n drops of this solution of oleic acid?
  5. What will be the volume of oleic acid in one drop of this solution?

How many astronomical units (A.U.) make 1 parsec?


Consider a sunlike star at a distance of 2 parsecs. When it is seen through a telescope with 100 magnification, what should be the angular size of the star? Sun appears to be (1/2)° from the earth. Due to atmospheric fluctuations, eye can’t resolve objects smaller than 1 arc minute.


Mars has approximately half of the earth’s diameter. When it is closest to the earth it is at about 1/2 A.U. from the earth. Calculate what size it will appear when seen through the same telescope.


Share
Notifications



      Forgot password?
Use app×