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A charge particle \( q_{0} \) of mass \( m_{0} \) is projected along the \( \mathrm{y} \)-axis at \( t=0 \) from origin with a velocity \( V_{0} \). If a uniform electric field \( E_{0} \) also exists along the \( x \)-axis, then the time at which debroglie wavelength of the particle becomes half of the initial value is :
(A) \( \frac{m_{0} v_{0}}{q_{0} E_{0}} \)
(B) \( 2 \frac{m_{0} v_{0}}{q_{0} E_{0}} \)
(C) \( \sqrt{3} \frac{m_{0} v_{0}}{q_{0} E_{0}} \)
(D) \( 3 \frac{m_{0} v_{0}}{q_{0} E_{0}} \)
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