Question

Derive debroglie wave equation for matter derive it for electrons mass m and accelerated by potantial v ​

Answer 1

Answer:

de Broglie equated the energy equations of Planck (wave) and Einstein (particle).

Explanation:

E=hv (planck's relation)

E=mc

2

(Einstein's mass - energy relation)

hv=mc

2

λ

hc

=mc

2

(or)

λ=

mc

h

For a particle moving with a velocity V,

λ=

mV

h

=

p

h

where p=mV is the momentum of the particle.

Solve any question of Dual Nature of Radiation And Matter with:-

Answer 2

Answer:

The de Broglie wavelength for electrons with mass m and accelerated by potential v ​ is $\frac{h}{\sqrt{2meV} }$

Explanation:

• The de Broglie wavelength is the wavelength of matter in wave nature

• For a particle with mass (m) and moving with velocity (v), the de Broglie wavelength is given by the formula

       λ =$h/p=h/mv$(equation 1)

      where Planck's constant $h=6.6*10^{-34}$

     $p$- the momentum of the particle

The kinetic energy of an electron with mass (m) and momentum (p) is $KE=\frac{p^{2} }{2m}$

⇒$p=\sqrt{2mKE}$

but the kinetic energy of an electron with charge(e) when accelerated to a potential(V)

is $KE=eV$

⇒ the momentum $p=\sqrt{2meV}$

put the value of momentum in equation 1

⇒λ= $\frac{h}{\sqrt{2meV} }$

which is the required wavelength