A charge particle $$q0$$ of mass $$m0$$ is projected along the $$y-axis$$ at t $$=$$ $$0$$ from origin with a velocity $$V0$$. If a uniform electric field $$E0$$ also exists along the $$x-axis$$, then the time at which debroglie wavelength of the particle becomes half of the initial value is $$Pm0v0q0E0$$ . Find the value of P.

Question

A charge particle $$q0$$ of mass $$m0$$ is projected along the $$y-axis$$ at t $$=$$ $$0$$ from origin with a velocity $$V0$$. If a uniform electric field $$E0$$ also exists along the $$x-axis$$, then the time at which debroglie wavelength of the particle becomes half of the initial value is $$Pm0v0q0E0$$ . Find the value of P.

Infinity Learn · Accepted Answer

Initial debroglie wavelength $$=hm0v0$$. Electric field will increase velocity in y direction,$$ay=q0E0mSo$$, $$vy=uy+ayt$$⇒$$vy=0+q0E0mtThus$$, momentum, $$Py=mvy=q0E0tTotal$$ momentum, $$P=Px2+Py2=m0v02+q0E0t2$$ After any time t,  λ$$=hm0v02+q0E0t2$$ When λ becomes half of the initial value : $$h2m0v0=hm0v02+q0E0t2$$⇒$$3m0v02=q0E0t2$$⇒$$t=3$$⋅$$m0V0q0E0$$

Wave nature of matter

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Wave nature of matter

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A charge particle q0 of mass m0 is projected along the y-axis at t = 0 from origin with a velocity V0. If a uniform electric field E0 also exists along the x-axis, then the time at which debroglie wavelength of the particle becomes half of the initial value is Pm0v0q0E0 . Find the value of P.

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