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Q.

 De Broglie’s relation is:

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a

λ=hmv

b

λ=hp

c

Both a and b

d

None of these

answer is C.

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Detailed Solution

Many ideas pertaining to the spectrum of various atoms and the splitting of spectral lines under magnetic and electric fields were not well explained by Bohr's model. There have been initiatives to create a more comprehensive atomic model in an effort to address the flaws in Bohr's atomic model. Analysis of the dual behaviour of matter was one of the breakthroughs that had a profound impact on formulation. De Broglie suggested that just as matter possesses both wave-like and particle-like characteristics, so does light. The dual behaviour of matter was used to characterizethe behaviorbehavior this nature. De Broglie developed a correlation between wavelength and matter momentum based on his findings. The de Broglie connection is the name given to this arrangement.

Given that particles are involved, Einstein's equation is as follows:

E=mc2-(1)
Where,
E= energy
m= mass
c= speed of light
According to Plank's equation, which takes into account the wave nature,
E=hv  ---(2)
Where,
E= energy
h= Plank's constant
v= frequency
From (1) and (2),
mc2=hv---(3)

Frequency, v can be expressed in terms of wavelength, λ as,
λ
For a general particle, c can be replaced with the velocity of an ,object, v. Hence, equation (3) can be given as,
mv=hvλ
λ=hmv

The wavelength,, is referred to as the de Broglie wavelength and the aforementioned equation as the de Broglie relationship. The de Broglie connection is explained by the diffraction of electron beams since diffraction is a characteristic of wave. An tool frequently used to demonstrate this fact is an electron microscope. As a result, every moving item has a wavelike quality. A huge mass causes the wavelengths connected with common things to be so short that it is impossible to detect their wave characteristics. On the other hand, it is possible to see experimentally the wavelengths connected to electrons and other subatomic particles.

Hence, the correct answer is option C.

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