Question 1
The wavelength of light of a particular colour is 5800 Ã….
Express it in —
(a) nanometer and
(b) metre
Answer
As we know, 1nm = 10 Ã…
Given,
The wavelength of light = 5800 Ã…
Substituting the value of wavelength in the relation above, we get,
10A˚=1nm
1A˚=10-¹nm
5800A˚=1/10×5800nm=580nm
Hence, wavelength of 5800 Ã… in nm = 580 nm.
(b) As we know,
1m = 10-¹⁰ Ã…
Given,
The wavelength of light = 5800 Ã…
Substituting the value of wavelength in the relation above, we get,
10¹⁰A˚=1m
1A˚=10−¹⁰m
5800A˚=5800×10−¹⁰m
⇒5800A˚=5.8×10−⁷m
Hence, wavelength of 5800 Ã… in m = 5.8 x 10 -⁷ m.
Question 2
The size of a bacteria is 1 µ. Find the number of bacteria in 1m length.
Answer
Given,
Size of a bacteria = 1 µ= 1 x 10-⁶ m
Total length = 1m
∴ Number of bacteria in 1m length = 1/10-⁶ = 10⁶.
Question 3
The distance of a galaxy from the earth is 5.6 x 10²⁵m. Assuming the speed of light to be 3 x 10⁸ ms-¹, find the time taken by light to travel this distance.
Hint —
Time taken=distance travelled/speed
Given,
distance = 5.6 x 10²⁵m
speed = 3 x 10⁸ ms-¹
Substituting the values in the formula above we get,
Time taken=5.6×10²⁵ x 3×10⁸
⇒Time taken=1.87×10¹⁷s
Time taken=3×10⁸ x 5.6×10²⁵⇒Time taken=1.87×10¹⁷s
∴, time taken by light = 1.87 x 10¹⁷s.
Question 4
The wavelength of light is 589nm. What is its wavelength in Ã…?
Answer
As we know, 1nm = 10 Ã…
Given,
The wavelength of light = 589nm
Substituting the value of wavelength in the relation above, we get,
589nm=589×10A˚
=5890A˚
Hence, the wavelength of light in Ã… is 5890 Ã….
Question 5
The distance of the nearest star, Proxima Centauri, from the Earth is 4.0 x 10¹³ km. Express it in light year.
Answer
1 Light year = 9.46 x 10¹² km
or 9.46 x 10¹² km = 1 Light year
∴ 4.0 x 10¹³ km
= 4.0 x 10¹³/ 9.46x 10¹²
= 4.2 light years.
Hence, distance of the nearest star from earth = 4.2 light years.
Question 6
It takes time 8 min for light to reach from the sun to the earth surface. If speed of light is taken to be 3 x 10⁸ms-¹, find the distance from the sun to the earth in km.
Answer
As we know, Distance = speed x time
Given,
Speed = 3 x 10⁸ ms-¹
Time = 8 min = 8 x 60s = 480s
Substituting the values in the formula above we get,
Distance = 3 x 10⁸ x 480 = 1440 x 10⁸ m.
= 1.44 x 10¹¹ m
∴,=1.44 x 10⁸ km
the distance from the sun to the earth is 1.44 x 10⁸ km.
Question 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.
Answer
'The distance of a star from the earth is 8.33 light minutes' implies, it takes 8.33 minutes for light to reach the earth from the star.
As we know,
Distance = speed x time
Given,
Speed = 3 x 10⁸ms-¹
Time = 8.33 min
= 8.33 x 60s
= 499.8s
≈ 500s
Substituting the values in the formula above we get,
Distance = 3 x 10⁸ x 500
= 1500 x 10⁸
= 1.5 x 10¹¹
∴, the distance from the star to the earth is 1.5 x 10¹¹m.
