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.

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