Engineering Physics BAS101: Notes for Unit 1 in Hinglish [AKTU]

Why Classical Mechanics Fails?

Why Classical Mechanics Fails?

Bhai, pehle ye samajh le ki classical mechanics (jo Newton ke laws par based hai) chhoti cheezon ke liye kaam nahi karti jaise atoms ya electrons. Kyun? Kyunki jab hum quantum level ki baat karte hain toh particles ka behaviour alag hota hai. Classical mechanics kehti hai ki hum kisi bhi object ki position aur momentum ek saath exact jaan sakte hain. Lekin quantum mechanics mein aisa nahi hota – yahaan Heisenberg ka Uncertainty Principle apply hota hai (isko hum aage detail mein padhenge).

For example, agar tum ek electron ko dekhoge, toh tum ye nahi bata sakte ki woh exact kahaan hai aur kis speed se move kar raha hai. Isliye jab atoms ya subatomic particles ki baat hoti hai toh classical mechanics fail ho jaati hai. Uske liye hume quantum mechanics chahiye!

Planck ka Black Body Radiation Theory (Qualitative)

Ab baat karte hain Planck ke theory ki. Bhai, ye Max Planck ne tab di thi jab usne dekha ki classical physics black body radiation ko explain nahi kar pa rahi thi. Black body kya hota hai? Ek ideal object jo sari energy ko absorb karta hai aur phir radiate bhi karta hai.

Classical theory ke according, ek black body ko bahut zyada ultraviolet light (short wavelength) radiate karni chahiye thi, par aisa nahi hua – isko bolte hain ultraviolet catastrophe. Tab Planck ne bola, “Energy continuous nahi hai, balki chhote chhote packets (quanta) mein aati hai.” In packets ko hum quanta bolte hain – aur yahin se quantum mechanics ka start hua.

Simple language mein: Energy ek baar mein chhoti-chhoti amounts mein nikalti hai, jaise chhote packets. Isne physics ki duniya badal di!

Compton Effect: Proof ki light particle jaise behave karti hai

Compton Effect kya hai? Ye ek experiment tha jisme Arthur Compton ne dikhaya ki light (jo hum wave maante the) particle ki tarah bhi behave kar sakti hai. Jab X-rays electrons par daagi gayi toh unki wavelength change ho gayi. Ye tabhi possible hai jab light ke particles (photons) electrons se takraate hain aur energy transfer karte hain.

Isse kya proof hua? Ki light ka dual nature hai – kabhi wave ki tarah behave karti hai, kabhi particle ki tarah. Ye concept quantum mechanics ka base ban gaya.

De-Broglie ki Matter Waves ki Concept

Ab yahaan se mazedaar part start hota hai! Louis de-Broglie ne bola: “Agar light wave aur particle dono ki tarah behave kar sakti hai, toh matter (jaise electron, proton) bhi kar sakta hai.” Usne matter waves ka concept diya. Har particle ke saath ek wave hoti hai – isko bolte hain De-Broglie wave.

Formula yaad rakho:

λ = h/p

Jahan: λ = wavelength, h = Planck’s constant, p = momentum

Yaani agar particle ka momentum kam hoga toh uski wavelength zyada hogi. Ye concept electrons ke behaviour ko samajhne ke liye bahut important hai.

Davisson aur Germer Experiment

Ye experiment de-Broglie ke idea ka proof tha. Davisson aur Germer ne electrons ko nickel crystal par daaga aur dekha ki electrons ne bhi waves ki tarah diffraction pattern banaya! Isse yeh pata chala ki electrons bhi wave-like behaviour dikhate hain, jaise de-Broglie ne bola tha.

Simple shabdon mein: Electron sirf particle nahi hai, wave bhi hai. Is experiment ne quantum mechanics ko solid proof diya.

Phase Velocity vs Group Velocity

Ab thoda technical part. Phase velocity aur Group velocity do tarike hain wave ki speed measure karne ke.

• Phase velocity: Ek single wave ki speed.

• Group velocity: Wave ke group (jaise matter waves) ki overall speed.

De-Broglie waves ke case mein, group velocity particle ki asli speed ke barabar hoti hai. Ye concept Schrödinger equation padhte waqt important hota hai.

Schrödinger Wave Equation: Quantum Mechanics ka Dil

Schrödinger Wave Equation quantum mechanics ka main part hai. Ye ek mathematical equation hai jo batata hai ki kisi particle ka wave function (ψ) time aur location ke saath kaise change hota hai. Iske do types hote hain:

1. Time-dependent Schrödinger Equation: Jab particle ka behaviour time ke saath badalta hai.

2. Time-independent Schrödinger Equation: Jab system stable hota hai, jaise atom ke andar electron.

Ye equation important kyun hai? Kyunki isse hum particle ki possible position aur energy calculate kar sakte hain.

Wave Function ki Physical Interpretation

Wave function (ψ) kya hota hai? Ye ek mathematical function hai jo particle ke behaviour ko describe karta hai. Iska physical matlab kya hai? |ψ|^2 (wave function ka square) batata hai ki particle kisi particular jagah hone ki kitni possibility hai.

Example: Agar kisi region ke liye |ψ|^2 bada hai, toh wahaan electron hone ki possibility high hai. Ye probability concept quantum mechanics ka ek important part hai.

Previous Year Questions and Answers for BAS101 Unit 1: Quantum Mechanics

Question 1:

Explain why classical mechanics fails at the atomic level. Discuss the need for quantum mechanics.

Answer:
Bhai, classical mechanics (Newton ke laws) badi cheezon ke liye perfect hai jaise car, ball wagairah. Par jab baat chhoti cheezon ki hoti hai jaise atom ya electron, toh yeh fail ho jaati hai. Kyun? Kyunki particles ka behaviour atomic level par alag hota hai.

Classical mechanics kehti hai ki hum particle ki position aur velocity dono exact ek saath jaansakte hain, lekin quantum level pe yeh possible nahi hota. Heisenberg ka Uncertainty Principle kehta hai ki position (x) aur momentum (p) ek saath accurate nahi jaane ja sakte.

Aur bhi reasons hain:

• Black body radiation ko explain nahi kar paayi (ultraviolet catastrophe wala problem).

• Atom ke spectrum ke specific lines kyun aate hain, iska answer nahi diya.

• Electrons ke wave-like behaviour ko ignore kiya.

Isliye hume Quantum Mechanics chahiye jo in saari cheezon ko explain karta hai — jaise dual nature (wave + particle) aur probability-based behaviour. Quantum mechanics ne physics ko naye tareeke se samjhaya!

Question 2:

Describe Planck's theory of black body radiation. How did it solve the ultraviolet catastrophe?

Answer:
Planck ki theory ne physics ki duniya hila di bhai! Black body ek aisi cheez hai jo saari energy absorb bhi karti hai aur radiate bhi.

Classical theory kehti thi ki black body se short wavelength (ultraviolet) light bahut zyada nikalni chahiye – par reality mein aisa nahi hota tha. Is problem ko Ultraviolet Catastrophe bolte hain.

Max Planck ne 1900 mein bola ki energy continuous nahi hoti, balki chhote-chhote packets (quanta) mein hoti hai.

Formula diya:

E = hν

jahaan:

• E = energy

• h = Planck constant (6.626 × 10⁻³⁴ J·s)

• ν = frequency

Is theory ne bataya ki high-frequency light ko radiate karne ke liye zyada energy chahiye hoti hai, isliye ultraviolet light zyada nahi nikalti. Isse ultraviolet catastrophe ka solution mil gaya – aur quantum mechanics ka foundation bana!

Question 3:

What is the Compton effect? Find the expression for the Compton shift.

Answer:
Compton Effect ne prove kiya ki light wave ke saath-saath particle (photon) ki tarah bhi behave karti hai. Jab X-rays electrons se takraayi, toh unki wavelength change ho gayi — isse bolte hain Compton Scattering. Arthur Compton ne 1923 mein ye experiment kiya tha.

Compton Shift ka Formula:

λ’ - λ = (h / m₀c) × (1 - cosθ)

jahaan:

• λ = incident wavelength

• λ’ = scattered wavelength

• h = Planck constant

• m₀ = electron ka rest mass

• c = speed of light

• θ = scattering angle

Yeh formula dikhata hai ki photon ki wavelength ka change kis angle par depend karta hai. Isse light ka dual nature (wave + particle) confirm ho gaya.

Question 4:

Explain the de-Broglie hypothesis of matter waves. How was it verified experimentally?

Answer:
1924 mein Louis de-Broglie ne bola ki agar light wave aur particle dono hai, toh matter (jaise electron, proton) bhi wave jaise behave kar sakta hai. Isne diya:

λ = h / p

jahaan:

• λ = wavelength

• h = Planck constant

• p = momentum = mv

Matlab: Har moving particle ke saath ek wave hoti hai. Chhote particles (electron wagairah) ke liye ye wavelength noticeable hoti hai.

Verification – Davisson-Germer Experiment (1927):
Davisson aur Germer ne electrons ko nickel crystal par fire kiya. Unhone dekha ki electrons diffraction pattern bana rahe hain — jo sirf waves banati hain. Inka result de-Broglie ke formula se match hua. Isse prove ho gaya ki electrons bhi wave-like behaviour dikhate hain.

Question 5:

Explain the difference between phase velocity and group velocity in the context of matter waves.

Answer:
Bhai ye thoda technical hai, lekin easy bana dete hain:

• Phase Velocity (vₚ): Ek single wave ki speed. Matter waves ke liye:
  vₚ = c² / v
  (c = light speed, v = particle velocity)
  Ye speed light ki speed se bhi zyada ho sakti hai, lekin isme energy ya information transfer nahi hoti.

• Group Velocity (v₉): Waves ke group ki overall speed. Matter waves ke liye ye particle ki asli speed ke barabar hoti hai.

Matlab:

• Phase velocity = mathematical concept (energy nahi le jaata)

• Group velocity = real speed of particle (information ya energy le jaata hai)