Question

what is de bronglie equation?
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Answer 1

De bronglie equation:

λ = h/mv

Meaning:

λ = wavelength

h = Planck's constant

m = mass of a particle

v = velocity

Explanation:

De bronglie equation is commonly used to define the wave properties of matter.

Answer 2

$\underline{\boxed{\bf{\red{De \: bronglie \: Equation:- }}}}$

This equation can be derived with the help of Planck's equation and Einstein equation.

According to Planck's Equation

• E = hv -------(1)

According to Einstein's Equation

• E = mc² ------(2)

Put the value of E in equation (2) from (1)

$\: \: \: \: \: \: \: \bold{mc {}^{2} = \: hv} \: \: \\ \rm{but \: v \: = \frac{c}{λ} } \\ \: \: \: \: \: \: \: \rm{now \: put \: the \: value \: of \: “v”} \\ \: \: \: \bold{\rm{mc {}^{2} = \frac{hc}{λ} }} \\ \: \: \: \rm{λ = \frac{h \cancel{c}}{mc {}^{ \cancel{2}} } } \\ \: \: \: \: \: \: \: \: : \rightarrow \boxed{ \rm{λ = \frac{h}{mc} }} -- (3)$

Equation (3) is called De bronglie equation.

De bronglie suggested that the same equation might be applied to material particles by considering m as mass of particle instead of the mass of proton and replacing c the velocity of the proton by v the velocity of the particles therefore equation (3) becomes :-

$\: \: \: \: \: \: \:\boxed{\rm{λ = \frac{h}{mv} }}--(4)\: \: \: \: \: \: \:$

Equation (4) is also called de bronglie equation.

But mv = Angular momentum it is denoted by p so,

$\: \: \: \: \: \: \:\bold{ λ= \frac{h}{p}}\: \: \: \: \: \: \:$

Where :-

• h = planck constant
• v = frequency
• m = mass of proton
• c = velocity of wave
• v = velocity of particle [use in eq. 4]
• λ = Wavelength

#Gunjan