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- 1. SO4: Matter waves What youwill learn 1. Properties of matter waves 2. Davisson and Germer experiment 3. Heisenberg’s What you already know 1. Light as an EM wave 2. Photon theory of light 3. Electron emission 4. Photoelectric effect 5. Radiation pressure
- 2. 𝑃 = = 𝐹 𝐼 𝐴 𝑐 For completeabsorption in normal incidence Absorption coefficient 𝑎 = 1 , Reflection coefficient (𝑟 = 0) For complete absorption in oblique incidence Absorption coefficient 𝑎 = 1 , Reflection coefficient (𝑟 = 0) � � 𝐹 cos 𝜃 𝐼 𝑃 = � � 2 = cos 𝜃
- 3. For partialreflection in normal incidence 0 < 𝑎 < 1, 0 < 𝑟 < 1 𝑎 + 𝑟 = 1 𝑃 = 𝐹 𝐼 𝐴 𝑐 = (1 + 𝑟) 𝑃 = 2 𝐼 � � For complete reflection in normal incidence Reflection coefficient (𝑟 = 1)
- 4. For partialreflection in oblique incidence 0 < 𝑎 < 1, 0 < 𝑟 < 1 𝑎 + 𝑟 = 1 𝑃 = 2𝐼 cos2𝜃 � � 𝑃 = 𝐹 𝐼 cos2𝜃 𝐴 𝑐 = (1 + 𝑟) For complete reflection in oblique incidence Reflection coefficient (𝑟 = 1)
- 5. a b c d 3.2 × 10−6 𝑁 1.6× 10−6 𝑁 4.3 × 10−8 𝑁 2 × 10−8 𝑁 A beam of white light is incident normally on a plane surface absorbing 70% of the light and reflecting the rest. If the incident beam carries 10 𝑊 of power , find the force exerted by it on the surface.
- 6. Force exerted byit on the surface is given by, � � � � Radiation falling perpendicularly = (1 + 𝑟) ⇒ = 𝐹 𝐼 𝐴 𝑐 𝐹 10 𝐴 𝐴𝑐 1 + 0.3 ⇒ 𝐹 = 1 3 3 × 108 = 4.3 × 10−8 𝑁 Solutio n Hence, option (𝑐) is the correct answer . Give n: 𝑎 = 0.7 𝑎 + 𝑟 = 1 ⇒ 𝑟 = 0.3 ⇒ 𝐼 = Power delivered by the incident beam = 10 𝑊 = 𝐼𝐴 10 � �
- 7. In 1924, theFrench physicist Louis Victor de-Broglie put forward the bold hypothesis that moving particles of matter should display wave like properties under suitable conditions. The waves associated with moving particles are called Matter waves or de-Broglie waves. The wavelength associated with a moving particle is known as de-Broglie wavelength. ℎ ℎ 𝜆 = = 𝑝 𝑚𝑣 𝑝 2 2 𝑚 𝐾. 𝐸. = ⇒ 𝑝 = 2𝑚 𝐾. 𝐸. 𝜆 = ℎ 2𝑚 𝐾. 𝐸. Where, p = Momentum
- 8. 𝜆 = ℎ When charge 𝑞accelerated through a potential difference 𝑉 from rest. Work done, 𝑊 = 𝐾. 𝐸. = 𝑞𝑉 2𝑚 𝑞𝑉 de-Broglie 𝜆 = ℎ 2𝑚 𝑞𝑉 𝜆 = 12.2 7 � � Å 𝜆 = ℎ 2𝑚 𝑞𝑉 = 6.62 ×10−34 2 × 9.1× 10−31×1.6 × 10−19 𝑉 ⇒ Mass of an electron, Charge on an electron,
- 9. An electron isaccelerated from rest through a potential difference of 𝑉 volt. If the de-Broglie wavelength of the electron is 1.227 × 10−2 𝑛𝑚, the potential difference is…. a b c d 10 𝑉 102 𝑉 103 𝑉 104 𝑉
- 10. de-Broglie wavelength, 𝜆= 1.227 × 10−2 𝑛𝑚 = 0.1227 𝐴 𝜆 = ℎ 2𝑚𝑒 𝑉 � � 12.27 = 𝐴 ⇒ 𝑉 = 12.2 7 0.122 7 = 100 Solutio n Give n: The de-Broglie wavelength of an electron is given by ⇒ 𝑉 = 104 𝑉 Hence, option (𝑑) is the correct answer .
- 11. a b c d The de-Broglie wavelengthof a neutron in thermal equilibrium with heavy water at a temperature 𝑇 (𝑘𝑒𝑙𝑣𝑖𝑛) and mass 𝑚, is …. ℎ 3𝑚𝑘 𝑇 2 ℎ 3𝑚𝑘 𝑇 2 ℎ 𝑚𝑘 𝑇 ℎ 𝑚𝑘 𝑇
- 12. Solutio n The average K.E.of gas molecules is given by, Wher e, 𝐽Τ 𝐾 𝑓 = Degree of freedom 𝑘 = Boltzmann constant = 1.38 × 10−23 𝑇 = Temperature in absolute scale For neutron, degree of freedom, 𝑓 = 3 ∴ K.E. of neutron, 3 2 𝐾. 𝐸. = 𝑘𝑇 de-Broglie wavelength is given by, 𝜆 = ℎ 2𝑚 𝐾. 𝐸. Substituting the value of K.E., we get, 𝜆 = ℎ 3𝑚𝑘 𝑇 Hence, option (𝑎) is the correct
- 13. Mass: 9.1 × 10−31𝑘𝑔 Speed: 3 × 106 𝑚/𝑠 Mass: 138 𝑔 Speed: 30 𝑚/𝑠 ℎ 6.63 × 10−34 𝜆 = = 𝑚𝑣 0.138 × 30 ℎ 6.63 × 10−34 𝜆 = = 𝑚𝑣 9.1 × 10−31 × 3 × 108 𝜆 = 1.6 × 10−34 𝑚 For macroscopic objects wave characteristics can not be 𝜆 = 2.42 × 10−9 𝑚 For microscopic particles wave Matter waves are related to moving particles and independent of the charge of particle. The phase velocity of matter waves can be greater than the speed of light. The wave and particle nature of moving bodies are mutually exclusive i.e., they can never be observed at the same time. Matter wave represents the probability of finding a particle in space. In ordinary situation, de-Broglie wavelength is very small and wave nature of matter can be ignored.
- 14. Itis not possibleto measure both theposition and momentum of a particle at the same time exactly. Uncertainty principle exists because everything in universe behaves both as particle and wave at the same time. Δ 𝑥 PARTICL E Δ𝑦 A particle exist in single place at any instant in time. � � � � A wave doesn’t exist at a single place, good probability of finding in lots of different places. We can measure its wavelength and thus its momentum.
- 15. ℎ 𝑝 = 𝑝= 𝑚𝑣 𝜆 A fast-moving object has lots of momentum, which corresponds to very short wavelength. A heavy object has lots of momentum, which again means a very short wavelength. This is the reason why we don’t notice the wave nature of everyday objects.
- 16. WAV E Momentum can be measured,but it has no definite position. PARTICL E Position can be measured, but it is difficult to measure momentum accurately. If Δ𝑥 is uncertainty in specification of position and Δ𝑝 is uncertainty in specification of momentum, then Δ𝑥 x Δ𝑝 ≥ ℎ 4 𝜋 Means if the position is measured very accurately then the momentum will have a lot of uncertainty and vice versa.