Question bank — Davisson-Germer experiment — electron diffraction

False. Ek special angle pe ek sharp intensity bump ke liye overlapping waves ki constructive interference chahiye; billiard-ball particles ek smooth featureless spread dete hain, isliye peak sirf wave ka signature hai.

False. Zyada $V$ ka matlab hai bada momentum $p=\sqrt{2meV}$, aur $\lambda =h/p$, isliye $\lambda$ kam hoti hai. Tez particles ki waves choti hoti hain.

False. Ye duality ki ulti direction prove karta hai — ki matter (electrons) wave ki tarah behave karta hai. Light-as-particle ka kaam Photoelectric effect ka hai.

True. Ek regular lattice ek well-defined atomic spacing deta hai, jisse scattered waves sharp predictable angles pe reinforce hoti hain; ek disordered tukde mein kai spacings milti hain aur peak wash out ho jaata hai.

False. Kinetic energy $54$ eV, electron rest energy $511,000$ eV ke muqable mein bilkul choti hai, isliye $v\ll c$ hai aur non-relativistic $p=\sqrt{2meV}$ essentially exact hai.

False. $\varphi$ incident beam se measure hota hai, $\theta$ crystal plane se; dono $\theta =90^{\circ }-\varphi /2$ se linked hain, barabar nahi hote.

True observed sense mein — real electrons discrete detected charges ki tarah aate hain (ye Wave-particle duality ka particle side hai) jinki statistical distribution wave pattern follow karti hai. Ek pure wave bina quantisation ke individual clicks nahi deti.

$0.91$ Å real Ni(111) plane spacing nahi hai ($d\approx 2.03$ Å); clean $1.65$ Å actually surface-grating relation $a\sin \varphi =n\lambda$ se aata hai jisme row spacing $a\approx 2.15$ Å hai, na ki Bragg se ek fudged $d$ ke saath.

Surface row se grazing scatter ke liye extra path $a\sin \varphi$ hai, $a\cos \varphi$ nahi. Cosine use karna peak ko galat angle pe predict karta.

Gain ki gayi energy $eV$ hai (charge times voltage), jo phir $\frac{1}{2}m{v}^2$ ke barabar hoti hai. Voltage $V$ ko speed $v$ se confuse karna do bilkul alag quantities ko mix karta hai.

Ye poora point hai, coincidence nahi: $\lambda$ ke do independent routes ka agree karna exactly wahi hai jo matter ke liye de Broglie hypothesis confirm karta hai.

Ye scattered current (kitne electrons) vs. angle measure karta hai. Wavelength baad mein geometry se infer ki jaati hai ki peak kahan hai.

Yahan electron–electron repulsion negligible hai; pattern tab aata hai jab har electron ki khud ki wave lattice se scatter hoke khud se hi interfere karti hai.

Diffraction tabhi observable, well-separated maxima produce karta hai jab grating spacing wavelength ke same order ki ho; $\lambda$ se bahut bada grating forward direction ke paas crammed peaks deta hai aur utterly weak features deta hai.

Ek road (theory, $\lambda =h/p$) assume karta hai ki de Broglie sahi hai; doosra (experiment, diffraction geometry se) nahi karta. Unka agreement hi test hai — ek single road hypothesis kabhi confirm nahi kar sakta.

Metal ko garam karne se electrons uski surface se boil off hote hain (thermionic emission), jo free electrons ki steady controllable supply deta hai accelerate karne ke liye.

Electrons crystal ke inner potential mein enter karte waqt thoda speed up ho jaate hain, jo surface ke andar unki wavelength thodi choti kar deta hai — ye ek small refraction correction hai jo vacuum formula mein nahi hai.

Ek narrow monoenergetic beam ek sharp wavelength aur ek incidence direction deti hai, isliye saari scattered waves same geometry share karti hain aur interference peak sharp rehti hai instead of smear hone ke.

Ye dono same ordered lattice ki do consistent geometric descriptions hain; har ek bas apna angle ek alag feature se reference karta hai (surface rows vs. internal planes), isliye dono same physics encode karte hain.

$\lambda$ shrink hoti rehti hai; first-order peak chote $\varphi$ ki taraf move karta hai aur, jab $\lambda$ itni choti ho jaaye ki woh order satisfy nahi kar sakta, woh peak bilkul disappear ho sakta hai jabki higher-order ones appear ho sakti hain.

$\lambda =12.27/\sqrt{V}$, $V\to 0$ ke saath without bound badhti hai; wavelength atomic spacing se bahut badi ho jaati hai, isliye koi diffraction maximum form nahi hota — geometry ab satisfy nahi ho sakti.

Nahi. Uska momentum enormous hai, isliye $\lambda =h/p$ atomic spacing ke muqable mein unimaginably chota hai, aur wave nature bilkul unobservable hai — isliye Wave-particle duality sirf tiny masses mein dikhti hai.

Koi single repeating spacing nahi hone se koi fixed path-difference condition nahi hai, isliye sharp peak ek broad diffuse halo mein dissolve ho jaata hai — lattice mein order ek sharp maximum ke liye essential hai.

Woh undeflected transmitted/reflected direction hai jahan har atom ke liye path difference zero hai; woh hamesha bright hota hai lekin koi wavelength information nahi deta, isliye woh diagnostic diffraction peak nahi hai.

Nahi — Bragg's law $2d\sin \theta =n\lambda$ sirf $\lambda$ aur spacing pe depend karta hai, na ki wave kis tarah ki hai; yahi equivalence exactly woh reason hai ki matter-wave diffraction X-ray diffraction ko mirror karti hai.