Derive debroglie relation.
Answers
Answer:
Because real particles do not travel at the speed of light, De Broglie submitted velocity (v) for the speed of light (c). Through the equation λ, de Broglie substituted v/λ for ν and arrived at the final expression that relates wavelength and particle with speed.
Answer:
Hello
Explanation:
E= mc2 —- (1)
Where,
E= energy
m= mass
c = speed of light
Considering the wave nature, the Plank’s equation is given as,
E = hν ——– (2)
Where,
E= energy
h = Plank’s constant
ν = frequency
From (1) and (2),
mc2 = hν ——– (3)
Frequency, ν can be expressed in terms of wavelength, λ as,
ν = cλ
For a general particle, c can be replaced with the velocity of object, v. Hence, equation (3) can be given as,
mv2 = hvλ
⇒λ = hmv
The above equation is known as de Broglie relationship and the wavelength, λ is known as de Broglie wavelength. Diffraction of electron beams explains the de Broglie relationship as diffraction is the property of waves. An electron microscope is a common instrument illustrating this fact. Thus, every object in motion has a wavelike character. Due to a large mass, the wavelengths associated with ordinary objects are so short that their wave properties cannot be detected. On the other hand, the wavelengths associated with electrons and other subatomic particles can be detected experimentally.