De Broglie hypothesis — matter waves λ = h - p: Foundations

2.3.5 · D1 · Physics › Modern Physics › De Broglie hypothesis — matter waves λ = h - p

Yeh page ek toolbox hai. Hum har symbol ko naam dete hain jinpar parent De Broglie topic depend karta hai, unke peeche ki picture draw karte hain, aur batate hain ki kyun topic unke bina aage nahi chal sakta. Top se bottom tak padho — har idea ek seedhi hai jis par agla khada hota hai.

0. Wave hoti kya hai (koi symbol se pehle)

Isse pehle ki hum keh sakein ki particle ki "wavelength hai," hume agree karna hoga ki wave kya hoti hai ek shape ki tarah.

Figure — De Broglie hypothesis — matter waves λ = h - p

Figure dekho. Curve crest tak uthti hai, trough tak girta hai, aur usi height par waapas aata hai us hi direction mein ja raha hai — woh repeat-distance is poore topic ki star hai.

1. $λ$ — the wavelength

s01 mein red bracket phir dekho: yeh exactly ek crest-to-crest gap span karta hai. Woh span $λ$ hai.

2. Units jinse hum baar baar milenge: ångström (Å)

3. Speed $v$ aur mass $m$ — ek chalte phirte lump ke paas jo do cheezein hoti hain

Yahan koi figure ki zaroorat nahi — yeh wahi everyday quantities hain jo ek 12-saal ka baccha pehle se jaanta hai: ek bhaari ball (bada $m$ ) zyada speed se phenki (bada $v$ ).

4. $p$ — momentum, woh "push" jo ek chalti cheez carry karti hai

$λ$ ke baad yeh topic mein sabse important quantity hai.

Figure mein, teen objects teen arrows carry karte hain. Har arrow ki length $p$ hai: truck (bada $m$ ) aur fast bullet (bada $v$ ) dono ko lambe arrows milte hain; slow feather ko ek chhota sa arrow milta hai.

5. $h$ — Planck's constant, woh tiny number jo quantum world chalata hai

Figure mein $λ = h / p$ ek curve ki tarah plot hai: jaise $p$ badhta hai (right ki taraf move karte hue), $λ$ zero ki taraf gir jaata hai. Do dots mark hain — electron (chhota $p$ , $λ \sim$ ångströms, visible) aur cricket ball (bahut bada $p$ , $λ \sim 1 0^{- 34}$ m, chart se bhi bahar chhota).

6. $ν$ , $c$ , $E$ — light-quantum symbols jinhe derivation borrow karti hai

Parent $λ = h / p$ ko pehle light se nikaal kar derive karta hai. Toh hume light ke teen symbols chahiye.

7. $γ$ aur "relativistic" — warning label

8. Symmetry idea — yeh sab propose kyun hua

Prerequisite map

Equipment checklist

Right side cover karo; kya tum read karne se pehle har ek answer de sakte ho?

λ

kya measure karta hai, aur wave par kis direction mein?

Repeat-distance (crest se agle crest tak), travel ke direction ke saath sideways measure kiya jaata hai; length ki units.

1 \overset{˚}{A}

kitne metres ke barabar hai, aur hum yeh kyun use karte hain?

1 0^{- 10}

m ≈ ek atom ki width; yeh atomic-scale wavelengths ko readable banata hai aur signal karta hai ki diffraction possible hai.

Momentum

p

ko words aur symbols mein define karo.

Chalti object ka "punch" = mass × speed,

p = m v

, units kg·m/s.

Kinetic energy

K

aur mass

m

ke terms mein

p

likho.

p = 2 m K

(

K = p^{2} /2 m

se).

h

ki value aur meaning batao.

h = 6.626 \times 1 0^{- 34}

J·s, Planck's constant — woh tiny "graininess" jo matter waves ko sirf bahut chhote

p

ke liye visible banati hai.

Cricket ball koi wave behaviour kyun nahi dikhati?

Uska

p

bahut bada hai, isliye

λ = h / p

around

1 0^{- 34}

m hota hai — observe karne ke liye kabhi bhi bahut chhota.

Teen light facts do jo derivation combine karta hai.

E = h ν

E = p c

c = ν λ

c = ν λ

obviously true kyun hai?

ν

wiggles of length

λ

har second guzarte hain, isliye distance per second =

ν λ

= speed.

p = m v

p = γ m v

se kab replace karna chahiye?

c

ke paas speeds par (relativistic); hamesha

λ = h / p

se shuru karo aur pehle

p

sahi nikalo.

Woh "symmetry" kya thi jisne de Broglie ko motivate kiya?

Agar light-waves particles ki tarah act karti hain, toh particles waves ki tarah act karni chahiye — even-handed wave–particle duality.