भूमी उपयोजन आणि भूमी आच्छादन फरक स्पष्ट करा
Answers
Answer:
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)
\begin{gathered} \: \: \: \: \: \: \: \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)\end{gathered}
mc
2
=hv
butv=
λ
c
nowputthevalueof“v”
mc
2
=
λ
hc
λ=
mc
2
h
c
:→
λ=
mc
h
−−(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)\: \: \: \: \: \: \:
λ=
mv
h
−−(4)
Equation (4) is also called de bronglie equation.
But mv = Angular momentum it is denoted by p so,
\: \: \: \: \: \: \:\bold{ λ= \frac{h}{p}}\: \: \: \: \: \: \:λ=
p
h
Where :-
h = planck constant
v = frequency
m = mass of proton
c = velocity of wave
v = velocity of particle [use in eq. 4]
λ = Wavelength