Numericals of Ex.-1(A) of chapter 1 (measurements and experimentation) of class-9.

 1. The wavelength of light of a particular colour is 5800 angstrom. Express it in a) nanometre     b) metre.

Ans. Wavelength of light=5800 A°

  Wavelength of light=5800 A°

               =5800× 10-¹⁰ m.   (1A° =10-¹⁰ m)

               =5800 ×10-¹-⁹ m   (x¹⁰=x¹ × x⁹)

               =5800× 10-¹ × 10-⁹ m

              =5800×1/10 × 1nm. (10-⁹ = 1 nm) (x-¹=1/x)

              =580×1 nm

              =580nm.

Wavelength of light=5800A°

     =5800× 1A°

    =5800 ×10-¹⁰ m. (1A°=10-¹⁰ m)

    =5.800×10³ ×10-¹⁰ m

   =5.8×10-⁷ m.    (x³-¹⁰ =x-⁷)

2. The size of a bacteria is one micrometre. Find the number of bacteria in 1 metre length .

Ans. The size of a bacteria is 1 micrometre.

Number of bacteria in 1 metre length=length/size of a bacteria.

The number of bacteria in 1 metre= 1m/10-⁶ m

       =1 × 10⁶   (1/10-⁶ = 10⁶ , m/m gets cancelled)

      =10⁶

3. The distance of a galaxy is 5.6 ×10²⁵ m. Assuming the speed of light to be 3×10⁸ m/s. Find the time taken by light to travel this distance?

Ans. Distance=5.6×10²⁵m

Speed=3×10⁸m/s.

Time=?

Speed=distance/time

Speed×time=distance

Time=distance/speed.

Time taken=5.6×10²⁵ m / 3×10⁸ ms-¹

              =5.6/3 × 10²⁵-⁸ s

             =1.8666 ×10¹⁷ s

             =1.87 × 10¹⁷ s.

4. The wavelength of light is 589 mm. What is its wavelength in angstrom?

Ans. The wavelength of light is 589 nm.

The wavelength of light= 589 nm.     

         =589×1nm

         =589×10-⁹ m  ( 1nm= 10-⁹m)

         =589× 10¹×10-¹ × 10-⁹ m

        = 5890 × 10-¹-⁹ m     (x-¹ × x-⁹ = x-¹⁰)

       =5890 ×10-¹⁰ m

       = 5890× 1 A°.      (1A⁰=10-¹⁰ m)

       =5890A°

5. The mass of an oxygen atom is 16.00 u. find its mass in kg?

Ans. The mass of an oxygen atom is 16.00 u.

Mass of oxygen atom=16.00 u

        =16.00 × 1 u

        = 16.00 × 1.66 × 10-²⁷ kg

       = 26.56× 10-²⁷ kg

       =2.656 ×10¹ × 10-²⁷ kg

       =2.656 × 10¹-²⁷ kg

       =2.656 × 10-²⁶ kg.

6. It takes time 8 minute for light to reach from the sun to the earth surface. If speed of light is taken to be 3×10⁸m/s. Find the distance from the sun to the earth in kilometre?

Ans. Time=8 minutes

                  =8×1minute

                  =8×60 s  (1 minute=60 seconds)

                 =480s

Speed=3× 10⁸ m/s.

Distance=?

Speed=distance/time.

Speed×time=distance

Distance=speed×time

Distance= 3× 10⁸ m/s × 480 s

                =3×480×10⁸ m

                =1440 × 10⁸ m

                =1.440×10³ ×10⁸m

                =1.440×10⁸ ×10³m

                = 1.440 × 10⁸ ×1km. (1000m=10³m=1km)

               =1.440 ×10⁸ km.

7. 'The distance of a star from the earth is 8.33 light minutes '.what do you mean by this statement? Express the distance in metre.

Ans. Distance of a star from the earth=8.33 light minutes.   

    Distance of a star from the earth=8.33 light minute

   = 8.33 ×3×10⁸ m/s × 1 minute

=8.33 × 3× 10⁸ m/s × 60 s.  (Speed of light=3×10⁸ m/s , 1 minute=60s)

=8.33×3×60 × 10⁸ m

=1499.4×10⁸ m

=1.4994 ×10³ ×10⁸ m

=1.5 × 10³+⁸ m.                    (1.4994 rounded as 1.5, x³ × x⁸ =x¹¹)

=1.5× 10¹¹ m.