**Dual Nature of Radiation and MatterÂ Important Questions for CBSE Class 12 Physics Matter Wave**

1.**Dual Nature of Radiation** Wave theory of electromagnetic radiation explained the phenomenon of interference, diffraction and polarisation. On the other hand, photoelectric effect supported particleâ€™s nature of light. Hence, we assume dual nature of light.

2.**de-Broglie Hypothesis** According to de-Broglie, wave is associated with moving matter which controls the particle in every respect.

**Previous YearsÂ Examination QuestionsÂ **

**1 Mark Questions**

**1.Write the expression for the de-Broglie wavelength associated with a charged particle having charge q and mass m, when it is accelerated by a potential [All India 2014]**

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**2.State de-Broglie hypothesis. [Delhi 2012]**

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**3.A proton and an electron have same kinetic energy. Which one has greater de-Broglie wavelength and why?Â ****[All India 2012]**

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**4.Write the relationship of de-BroglieÂ wavelength X associated with a particle of mass m in terms of its kinetic energy E .Â Â [Delhi 2011c]**

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**5.Show graphically, the variation of de-Broglie wavelength (A,) with the potential (V) through which an electron is accelerated from rest.Â [Delhi 2011]**

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**6.Name an experiment which showsÂ wave nature of the electron. Which phenomenon was observed in this experiment using an electron beam? Â [Foreign 2010]**

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**7.An electron and a-particle have the same kinetic energy. How are the de-Broglie wavelengths associated with them related?Â [Delhi 2008]**

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**2 Marks Questions**

**9. A proton and a deuteron are accelerated through the same accelerating potential. Which one of the two has**

**greater value of de-Broglie wavelength associated with it and****less momentum?Â****Give reasons to justify your answer.Â Â Â Â Â Â Â Â Â [Delhi 2014]**

**Ans.**

**10.A deuteron and an a-particle are accelerated with the same accelerating potential. Which one of the two has**

**greater value of de-Broglie wavelength, associated with it and****less kinetic energy? Explain. Â [Delhi 2014]**

**Ans.**

**11.X-rays fall on a photosensitive surface to cause photoelectric emission. Assuming that the work-function of the surface can be Â neglected, find the relation between the de-Broglie wavelength (A,) of the electrons emitted to the energy (E _{v}) of the incident photons. Draw of the graph for A, as function of E_{v}.Â [Delhi 2014 C]**

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**12.An electron is revolving around the nucleus with a constant speed of 2.2 xlO ^{8} m/s. Find the de-Broglie wavelength associated with it.Â [All India 2014 C]**

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**13.An a-particle and a proton are accelerated from rest by the same potential. Find the ratio of their de-Broglie wavelengths.Â [All India 2010; Foreign 2008]**

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**14.An electron is accelerated through a potential difference of 100 V.Â What is the de-Broglie wavelength associated with it? To which part of the electromagnetic spectrum does this value of wavelength correspond? [Delhi 2010]**

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**15.An electron is accelerated through aÂ potential difference of 144 V. What is the Â de-Broglie wavelengthÂ ****associated with it? To which part of electromagnetic spectrum does this wavelength correspond? [Delhi 2010]**

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**16.An electron is accelerated throughÂ a potential difference of Â 64 VÂ What is the de-Broglie wavelength associated with it? To which part of the electromagnetic spectrum does this value of wavelength correspond?Â [Delhi 2010]**

**Ans. Â **Refer to ans 14

**17.Find the ratio of de-Broglie wavelengths associated with**

**protons, accelerated through a potential of 128 V and****a-particles, accelerated through a potential of 64 V. [HOTS; Delhi 2010C]**

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**18.The ratio between the de-BroglieÂ wavelengths associated with protons, accelerated through a potential of 512 V and a-particles, accelerated through a potential of X volt is found to be one. Find the value of X.Â Â Â Â [Delhi 2010c]**

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**20.Derive an expression for the de-Broglie wavelength associated with an electron accelerated through a potential V.Â Draw a schematic diagram of a localised wave describing the wave nature of the moving electron.Â Â Â Â Â [Foreign 2009]**

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**21.Calculate the ratio of the acceleratingÂ potential required to accelerate a proton and an cx- article to have the same de-Broglie wavelength associated with them. Â Â Â Â [Delhi 2009C]**

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**22.Calculate the ratio of the accelerating potential required to accelerate a deuteron and an a-particle to have the same de-Broglie wavelength associated with them. (Given, mass of deuteron = 3.2 x 1CT ^{27} kg)Â [Delhi 2009C]**

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**23.Crystal diffraction experiments canÂ be performed either by using electrons accelerated through appropriate voltage or by using X-rays. If the wavelength of these probes (electrons or X-rays) is 1 A, estimate which of the two has greater energy.Â [All India 2009]**

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**24.In Davisson-Germer experiment, state the observations which led to**

**show the wave nature of electrons and****confirm the de-Broglie relation. Â [Delhi 2008]**

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**25.For what kinetic energy of a neutron will the associated de-Broglie wavelength be 1.32 x 10 ^{-10} m?Â [All India 2008]**

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**26.An electron and a-particle have the same de-Broglie wavelength with them. How are their kinetic energies related to each other?Â [Delhi 2008]**

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**27.For what kinetic energy of a neutron, will the associated de-Broglie wavelength beÂ 1.32 x 10 ^{_1}Â° m? Given that the mass of a neutron = 1.675 xlO^{-27} kg.Â [All India 2008C]**

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**3 Marks Questions**

**28.An electron microscope uses electrons accelerated by a voltage of 50 kV. Determine the de-Broglie wavelength associated with the electrons. Taking other factors, such as numerical aperture, etc., to be same, how does the resolving power of an electron microscope compare with that of an optical microscope which uses yellowÂ light? Â Â Â Â Â [All india 2014]**

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**29.(i) Describe briefly how theÂ Davission-Germer experiment demonstrated the wave nature of electrons.**

**(ii) An electron is accelerated from rest through a potential V, obtain the expression for the de-Broglie wavelength associated with it.**

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**30.Determine the de-BroglieÂ wavelength of a proton whose kinetic energy is equal to the rest mass energy of an electron. Mass of a proton 1836 times that of electron, (ii) In which region of electromagnetic spectrum does this wavelength lie?Â [All India 2011C]**

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**31.The mass of a particle moving withÂ velocity 5 x 10 ^{6} m/s has de-Broglie wavelength associated with it to be 0.135 nm. Calculate its mass.**

**(ii) In which region of the electromagnetic spectrum does this wavelength lie?Â [All India 2011C]**

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**33.An electron and a photon each have a wavelength lnm. FindÂ [Ail India 2011C]**

**their momenta****the energy of the photon and****the kinetic energy of electron.**

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**34.A proton and an a-particle are accelerated through the same potential. Which of the two has ‘**

**greater value of de-Broglie wavelength associated with it and****less kinetic energy?Â****Justify your answer. [Delhi 2009]**

**Ans.**

**35.An electron and a proton are accelerated through the same potential. Which one of the two has**

**greater value of de-Broglie wavelength associated with it and****less momentum?Â****Justify your answer. [Delhi 2009]**

**Ans.**

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