Question

Anyone please give the important derivatins in dual nature of radiation and matter​

Answer 1

Explanation:

E=hv.....1

According to Einstein

E= mc^ 2 •••• 2

combining the above two eq. 1 and 2

we get:

hv= mc^2

Now, since v lambda=c

v= c/ lambda

hc/ lambda= mc^ 2

h/ lambda= mc

lambda= h/ mc

Answer 2

★☆〖Qบęຮτ ı¨ ø nˇ〗☆★

⭐The Dual Nature of Matter⭐

=> de-Broglie's Principle states that "All material particles in motion possess wave characteristics..."

=> de-Broglie's Relationship can be derived by combining the mass and energy relationships proposed by Max Planck, and Albert Einstein...

E = ∫c²dm = Σc²Δm = mc²

E = hν

=> The combination of these two yielded the desired result:

λ = h/mc

=> The above equation is valid for a Photon(γ⁰)

=> The same relation can be extended to every particle of this universe, if the speed of light in vacua(c) is replaced by the ordinary velocity of the particle:

$\: \: \: \: \: \: \: \: \: λ = \frac{h}{ \: mv⃗}$

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