## FSc ICS Notes: Physics XII: Chapter 19 Dawn of Modern Physics Exercise Short Questions:

**Question**19.1 What are measurements on which two observers in relative motion always agree upon?**The measurements of**

**Answer**19.1- force
- acceleration
- velocity of light

**Question**19.2**Does the dilation means that time really passes more slowly in moving system or that it only seems to pass more slowly?**

**The time dilation is purely due to relative motion. It really happen when observers are in relative motion. The result is applied to the timing process physical, chemical and biological. Even aging process of the human body is slowed down by motion at very high speed. It should be noted that we can not detects such changes in daily life because we are not moving at speed comparable to the speed of the light.**

**Answer**19.2

**Question**19.3 If you are moving in a spaceship at a very high speed relative to the Earth, would you notice a difference (a) in your pulse rate (b) in the pulse rate of people on Earth?**The pulse rate of the person in spaceship is the proper pulse rate. There will be no difference in the pulse rate as the inertial frame of reference is same. Pulse rate of the people on the earth will be low because they are moving with respect to spaceship.**

**Answer**19.3

**Question**

**19.4**

**If the speed of light were infinite, what would the equations of special theory of relativity reduce to?**

**When the speed of light approached to infinity.**

**Answer**19.4m = m, l = l, t = t , c = ∞.

m = mo

**/**(√ 1 – v2 /∞) = mo

**/**(√ 1 – 0) = mo.

l = lo (√ 1 – v2 /∞) = lo (√ 1 – 0) = lo.

t = to

**/**(√ 1 – v2 /∞) = to

**/**(√ 1 – 0) = to.

E = m (∞)Square ⇒ E is infinity.

**Question**19.5 Since mass is a form of energy, can we conclude that a compressed spring has more mass than the same spring when it is not compressed?**From classical point of view the mass remain same. According to theory of relativity, change of mass is due to relative motion and not due to position.**

**Answer**19.5

**Question**19.6**As a solid is heated and begins to glow, why does it first appear red?**

**According to wien's displacement law at low temperature the solid will emit radiation having longer wavelength which lies in the infra-red region of electromagnetic spectrum. That is why the appearance of the body will be red when it begins to glow. On further increasing the temperature, the solid will change the color towards decreasing wavelength of visible spectrum.**

**Answer**19.6

**Question**19.7**What happens to total radiation from a black body if its absolute temperature doubled?**

**According to Stefen Boltzmann law, the amount of energy radiated per sec per unit area pf the black body is directly proportional to the fourth power of its absolute temperature i.e.**

**Answer**19.7E = Ïƒ T4

It is obvious that if temperature T is doubled, E becomes 16 times of the original radiant energy.

**Question**19.8 A beam of red light and a beam of blue light have exactly the same energy. Which beam contains the greater number of photons?**The energy of the photon of light by Planck quantum theory is given by:**

**Answer**19.8**E = hf**

Where h is the Planck constant and f is the frequency of light. Let n1 be the number of photons of red light having frequency f1 and n2 be the number of photons of blue light having frequency f2. The respective energies of red and blue beams of light is given be:

E1 = n1 h f1

E2 = n2 h f2

E1 = E2

n1 h f1 = n2 h f2

f1 / f2 = n1 / n2

f1 < f2

n2 < n1

i.e. number of photons of red light are more than the number of photons of blue light.

**Question**19.9 Which photon, red, green, or blue carries the most (a) energy and (b) momentum?**The expression for energy and momentum of photons are given by**

**Answer**19.9E = hf

p = hf / c

as f = c / Î»

therefore E = hc / Î»

and p = h / Î»

Blue light has smaller wavelength than red and green colors. So energy and momentum of photons of Blue light is greater than green and red.

**Question**19.10**Which has the lower energy quanta? Radio waves or X-rays.**

**By Plank quantum theory the energy of the quanta of radiation is given by,**

**Answer**19.10E = hf

Since the frequency of x-rays is greater than the frequency of radio wave therefore, the quanta of x-ray will carry more energy than that of radio wave.

**Question**19.11 Does the brightness of a beam of light primarily depends on the frequency of photons or on the number of photons?**Brightness or intensity of light beam of specific color means the number of photons of light passing per sec per unit area. So, brightness depends upon numbers of photons and not on frequency of photons.**

**Answer**19.11

**Question**19.12**When ultraviolet light falls on certain dyes, visible light is emitted. Why does this not happen when infrared light falls on these dyes?**

**The ultraviolet light contains photons of high energy. When they fall on the atoms of the dye, the atoms get excited. On De-excitation they emit photons of frequency which lie in visible region of electro-magnetic spectrum. However infra-red light photon has less energy, so the atoms may be excited, on De-excitation they emit photons whose frequency lie in the invisible region.**

**Answer**19.12

**Question**19.13**Will bright light eject more electrons from a metal surface than dimmer light of the same color?**

**The number of photo-electrons emitted from the metal surface is proportional to the intensity of light. So, bright light eject more electrons from metal surface than the dimmer light of same color.**

**Answer**19.13

**Question**19.14 Will higher frequency light eject greater number of electrons than low frequency light?**The number of photo electrons emitted from the metal surface is directly proportional to the intensity of incident light and not on its frequency. The light of higher frequency light will eject energetic electrons, while low frequency light will eject less energetic electrons. So light of higher and lower frequency of same intensity will eject same number of electrons.**

**Answer**19.14

**Question**19.15**When light shines on a surface, is momentum transferred to the metal surface?**

**When light falls on metal surface, the photons are absorbed by the surface. Therefore both energy and momentum of the photons are transferred to the atoms of the surface. The exchange of energy and momentum to the surface is so small that it hardly produce any disturbance in photo emissive surface.**

**Answer**19.15

**Question**19.16**Why can red light be used in a photographic dark room when developing films. blue or white light cannot?**

**Photons of red light in visible spectrum has the longest wavelength and the least energy. Therefore photographic films and materials concerned are least affected in the presence of red light than blue and white light.**

**Answer**19.16

**Question**19.17**Photon A has twice the energy of photon B. What is the ratio of the momentum of A to that of B?**

**As we know that:**

**Answer**19.17EA = hfA = hc / Î»A

and EB = hc / Î»B

since EA = 2EB

hc / Î»A = 2(hc / Î»B)

Î»B = 2Î»A

momentum of photon B is given by:

pB = h / Î»B

putting Î»B = 2Î»A

pB = h / 2Î»A

as h / Î»A = pA (momentum of photon A)

pB = 0.5pA

or pA = 2pB

pA / pB = 2 / 1

pA : pB = 2 : 1

**Question**19.18**Why don’t we observe a Compton effect with visible light?**

**Photons of visible light (violet) are most energetic and have energy:**

**Answer**19.18E = hc / Î» = {6.6 * 10(-34) x 3 * 10(8)} / 400 * 10(-9) J

E = {6.6 * 10(-34) x 3 * 10(8)} / 400 * 10(-9) x 1 / 1.6 * 10(-19) eV

E = .310 KeV

But for Compton effect energy more than .1 MeV is needed, so Compton effect cannot be studied with visible light.

**Question 19.19 Can pair production take place in vacuum? Explain.**

**Pair production takes place near the nucleus which takes recoil to conserve momentum. Thus law of conservation of momentum will be violated if pair production takes place in vacuum. Hence pair production cannot take place in vacuum as it does not contain matter.**

**Answer**19.19

**Question**19.20 Is it possible to create a single electron from energy? Explain.**No, it is not possible, because law of conservation of charge will be violated when single electron will be created.**

**Answer**19.20

**Question**19.21 If electrons behaved only like particles, what pattern would you expect on the screen after the electrons passes through the double slit?**When electrons have particles like property diffraction will not take place and electrons would pass straight through the slits. Therefore the diffraction pattern on the screen will not be observed. We will only observe the images of two slits on the screen.**

**Answer**19.21

**Question**19.22 If an electron and a proton have the same de Broglie wavelength, which particle has greater speed?**As we know that momentum:**

**Answer**19.22p = mv = h / Î»

or v = h / mÎ»

as same Î» & h , and Î» being constant

v ∝ 1 / m

From above equation it follows that electron being lighter particle will have greater speed than proton to have same value of de Broglie wavelength.

**Question**19.23 We do not notice the de Broglie wavelength for a pitched cricket ball. Explain why?**According to de Broglie, the wavelength of the particle of mass m when moving woth velcity v is given by:**

**Answer**19.23Î» = h / mv

It follows that wavelength Î» is inversely proportional to the mass of the particle. The cricket ball is very much massive, so it has very short wavelength which is not measurable.

**Question**19.24 If the following particles all have the same energy, which has the shortest wavelength? Electron, alpha particle, neutron, proton.**From the relation:**

**Answer**19.24Î» = h / mv

for same energy (or K.E.) v & h are constant, so

Î» ∝ 1 / m

It follows from the above relation that for greater mass there is shorter wavelength. As Î±-particle has greatest mass, so the Î±-particle has the shortest wavelength and the electron of smallest mass has the largest wavelength associated with it.

**Question**19.25 When does light behave as a wave? When does it behave as a particle?**In case of interference and diffraction phenomena light behaves as waves. In phenomena like photoelectric and Compton effects, the light exhibits its particle nature.**

**Answer**19.25**What advantages an electron microscope has over an optical microscope?**

**Question**19.26**The electron microscope has the following advantages over optical microscope.**

**Answer**19.26- The wavelength associated with electron is much shorter than the visible light, so electron microscope has high resolving power as compare to optical microscope.
- The energy of electrons is sufficiently large that they can penetrate through the thicker parts of matter as compared to visible light. Therefore the internal structure of an object can be obtained by Electron microscope.

**Question**19.27**If measurements show a precise position for an electron, can those measurements show precise momentum also? Explain.**

**Answer 19.27**No. According to Uncertainty principle, position and momentum of a particle cannot both be measured simultaneously with perfect accuracy. For a precise position of an electron, the momentum becomes uncertain.

Î”x • Î”p ≈ h

If the position of an electron is precisely measured then there is not uncertainty in position i.e.,

Î”x = 0,

0 • Î”p ≈ h

or Î”p ≈ h / 0 ≈ ∞

So, if measurement show a precise position for electron in an experiment then precise measurement of momentum of an electron is impossible in that experiment.

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