Skip to main content

National Bird Day: Why Birds Matter to Us

National Bird Day is celebrated every year on 5 January . This day is observed to spread awareness about birds, their importance in nature, and the need to protect them. Birds are beautiful living beings and play a very important role in keeping our environment healthy. Origin of National Bird Day National Bird Day was first celebrated in the year 2002 . It was started by bird lovers and environmental groups to protect birds from dangers like deforestation, pollution, and illegal hunting. The main aim of this day is to teach people, especially students, why birds are important and how we can help save them. Why Is National Bird Day Celebrated Every Year? National Bird Day is celebrated every year because many bird species are disappearing due to human activities. Cutting trees, using plastic, pollution, and climate change are harming birds and their homes. This day reminds us that: Birds need protection Nature should be respected Everyone has a responsibil...
Post a Comment

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
Labels:

Comments

Post a Comment

Popular posts from this blog

Electric field due to circular loop of charge | Electromagnetics

Electric field due to circular loop of charge Electric field The space around a charged particle in which another charge experience a force is known as electric field. The source of electric field is either a charge or a time varying magnetic field. If the value of electric field does not change with time, then it will be uniform electric field, otherwise it will be non-uniform electric field. Electric field due to circular loop of charge If λ is linear charge density, then the charge on d l dq = λ d l      ⇒     dq = (q / 2πa) d l Electric field at P due to charge dq Special cases When P lies at the centre of the loop i. e., r = 0, then E = 0 When P lies very far from the centre of the loop i. e., r >> a, then E = kq / r 2 In this case circular loop behaves as a point charge. To know more about this topic please click on the link  https://youtu.be/54MIe0Ow43w   or...
Post a Comment
Read more

Advanced Calculus | Mathematics | BSc

Advanced Calculus Advanced Differential Calculus, Integral Calculus and Vector Calculus Authors: Dr. Vimal Saraswat, Dr. Anil Kumar Menaria ISBN : 978-81-7906-950-9 Price: Rs. 375.00 Publisher: Himanshu Publications, Hiran Magri Udaipur; Himanshu Publications Prakash House, Ansari Road, New Delhi E-mail :  info@sacademy.co.in Phone:  +91 9664392614 To buy this book click on the link Advanced Calculus by Saraswat This book includes the following topics  Continuity Introduction Limit Left and right limit To find the R.H.L. and L.H.L. of a function Existence of limit)/li> Distinction between the value and limit of a function Some theorems based on limits Methods of finding the limit of functions Some standard limits Cauchy’s definition of continuity Continuity from left and right Continuity of a function in an interval Continuity in the open interval); Continuity in the closed in...
Post a Comment
Read more

आवेश तथा उसके गुण | Charge and its properties in Hindi

आवेश तथा उसके गुण आवेश क्या है कोई नहीं जानता कि आवेश क्या है, केवल हम यह जानते हैं कि आवेश क्या कर सकता है तथा इसके गुण क्या हैं ? आवेश के प्रकार आवेश दो प्रकार के होते हैं, धनावेश तथा ऋणावेश। धनावेश प्रोटॉन के कारण होता है तथा ऋणावेश इलेक्ट्रॉन के कारण। तीसरे प्रकार का कोई आवेश ब्रहाण्ड में विद्यमान नहीं है। आवेश का क्वांटीकरण आवेश सदैव पैकेट के रूप में होता है, सतत्‌ नहीं। किसी वस्तु को दिया गया आवेश सदैव एक न्यूनतम आवेश का पूर्ण गुणज होता है यह न्यूनतम आवेश इलेक्ट्रॉन के आवेश के बराबर होता है, जिसका मान e = 1.6*10 -19 C होता है। q = ne,        यहां n = 0, 1, 2, ... आवेश संरक्षण का नियम आवेश को न तो उत्पन्न किया जा सकता है तथा न ही नष्ट किया जा सकता है, परन्तु इसे निकाय के एक भाग से दूसरे भाग में स्थानान्तरित किया जा सकता है। किसी विलगित निकाय का आवेश सदैव संरक्षित रहता है। Σq i = नियत,           यहां q i = iवे कण का आवेश आवेश के गुण स्थिर विद्युत आव...
Post a Comment
Read more