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Bhupal Nobles' University, Udaipur Convocation | भूपाल नोबल्स विश्वविद्यालय, उदयपुर दीक्षांत समारोह

भूपाल नोबल्स विश्वविद्यालय दीक्षांत समारोह महाराणा प्रताप स्टेशन रोड, सेवाश्रम सर्कल, उदयपुर। भूपाल नोबल्स विश्वविद्यालय उदयपुर द्वारा वर्ष 2018 से 2024 तक की स्नातक एवं स्नातकोत्तर परीक्षा में उत्तीर्ण एवं विद्यावाचस्पति (Ph.D.) उपाधिधारियों के लिए दीक्षान्त समारोह 27 मार्च 2025 गुरूवार को प्रातः 10:30 बजे आयोजित करने का निश्चित हुआ है। दीक्षान्त समारोह में 2020 से 2025 तक की विद्यावाचस्पति की उपाधियों तथा स्नातक एवं स्नातकोत्तर परीक्षाओं में वर्ष 2024 तक प्रथम स्थान प्राप्त करने वाले छात्रों को उपाधि एवं स्वर्ण पदक प्रदान किए जायेंगे। अतः जो उपाधिधारी उक्त समारोह में उपाधि प्राप्त करने के इच्छुक हों, वे समारोह में उपस्थित होने की लिखित सूचना के साथ स्नातक एवं स्नातकोत्तर प्रथम वरीयता प्राप्त छात्रों हेतु, पंजीकरण शुल्क ₹500 व उपाधि शुल्क ₹5000 (कुल ₹5500) एवं विद्यावाचस्पति (Ph.D.), शोधार्थी पंजीकरण शुल्क ₹500 व उपाधि शुल्क ₹5000 (कुल ₹5500) नकद अथवा डिमाण्ड ड्राफ्ट भूपाल नोबल्स विश्वविद्यालय, उदयपुर के नाम बनाकर कुलसचिव, भूपाल नोबल्स विश्वविद्यालय, उदयपुर को दिनांक 17.03.2025 तक ...
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de Broglie hypothesis | Quantum mechanics | Physical basis of quantum mechanics

de Broglie hypothesis

  • According to de-Broglie, a wave is always associated with every moving particle. This wave is known as de-Broglie wave or matter wave.
  • It means a matter wave have particle nature as well as wave nature i.e., dual nature.
  • From quantum theory of radiation, energy of photon, E = h𝝂,   where 𝝂 = frequency of incident photon .
  • From Einstein’s theory of relativity E = √(m02c4 + p2c2)
  • If m0 = 0, then E = pc,  p = momentum and c = velocity of light
  • Now E = h𝝂 and E = pc
  • ∴     h𝝂 = pc     or     p = h𝝂/c
  • ∵      c = 𝝂λ      or     λ = c/𝝂
  • ∴      p = h/λ     or     λ = h/p     This is known as de-Broglie wavelength
  • This wavelength is always associated with a photon
  • Since momentum is the characteristic of particles, and the wavelength is characteristic of wave.
  • Hence a wave is always associated with a particle.

Conclusion

  • The wavelength of a particle is independent of the charge or the nature of the particle.
  • The E.M. waves are produced only due to the charged particle. Hence the matter waves are not E.M. in nature.
  • ∵     λ = h/p    and   p = mv      ⇒     λ ∝ 1/v    and   λ ∝ 1/m,      v = velocity of particle 
  • Faster is the particle, smaller is its wavelength.
  • Heavier is the particle, smaller is its wavelength.
  • If v is comparable to c, then m = m0/√(1 − v²/c²) 
                

de Broglie wavelength of different particles

  • If an electron is accelerated by applying a potential difference V, then 
  • Energy acquired with it is E = eV
  • If m0 is rest mass of electron, and v is the velocity of electron, then 
  • Kinetic energy of electron, E = ½ m0v²    or   v = √(2E/m0)
  • If relativistic variation of mass with velocity is ignored m ≈ m0 
  • ∴     v = √(2E/m)
  • But  E = eV
  • ∴     v = √(2eV/m)
  • ∵     de-Broglie wavelength λ = h/mv and v = √(2eV/m)
  • ∴     λ = h/√2meV      or      λ = 12.27/√V  Å
  • For any charged particle    λ = h/√2mqV
  • For any massive particle    λ = h/√2mE            where E is kinetic energy
  • If a matter particle at absolute temperature T is in thermal equilibrium, then 
  • E = 3/2 kT      where   k = Boltzmann's constant and T is absolute temperature
  • ∵     λ = h/√2mE     ∴   λ = h/√3mkT

  Bohr’s hypothesis from de Broglie’s hypothesis

  • According to Bohr’s postulate, an electron can revolve around the nucleus only in those orbits whose angular momentum is an integral multiple of h/2π.
  • ∴     mvr = nh/2π
  • Since a wave is associated with a moving particle, so 2πr = nλ
  • Here 2πr is the circumference of the stable orbit
  • From de-Broglie hypothesis,  λ = h/mv
  • Now 2πr = nλ  and  λ = h/mv
  • ∴     2πr = nh/mv ⇒ mvr = nh/2π
  • Which is the Bohr's hypothesis

To know more about this lecture please visit on https://youtu.be/PFcQEKaX1fc
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