A proton and an alpha-particle are accelerate | vedclass

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(C) The de Broglie wavelength $\lambda$ of a particle accelerated through a potential difference $V$ is given by $\lambda = \frac{h}{\sqrt{2mQV}}$.Sin

Vedclass · Accepted Answer

$2\sqrt{2} : 1$

Vedclass · Answer

(C) The de Broglie wavelength $\lambda$ of a particle accelerated through a potential difference $V$ is given by $\lambda = \frac{h}{\sqrt{2mQV}}$.Since $h$ and $V$ are constant for both particles,we have $\lambda \propto \frac{1}{\sqrt{mQ}}$.Therefore,the ratio of the wavelength of the proton $(\lambda_p)$ to that of the $\alpha$-particle $(\lambda_\alpha)$ is $\frac{\lambda_p}{\lambda_\alpha} = \sqrt{\frac{m_\alpha Q_\alpha}{m_p Q_p}}$.Given that the mass of an $\alpha$-particle $m_\alpha = 4m_p$ and its charge $Q_\alpha = 2Q_p$,we substitute these values:$\frac{\lambda_p}{\lambda_\alpha} = \sqrt{\frac{4m_p 	imes 2Q_p}{m_p 	imes Q_p}} = \sqrt{8} = 2\sqrt{2}$.Thus,the ratio is $2\sqrt{2} : 1$.

Column $I$	Column $II$
$(a)$ Proliferative Phase	$(i)$ Breakdown of endometrium
$(b)$ Secretory Phase	$(ii)$ Follicular phase
$(c)$ Menstruation	$(iii)$ Luteal Phase

$A$ proton and an $\alpha$-particle are accelerated through a potential difference of $100 \ V$. The ratio of the wavelength associated with the proton to that associated with an $\alpha$-particle is

Similar Questions

Match the items given in Column $I$ with those in Column $II$ and select the correct option given below:

Column $I$ Column $II$

$(a)$ Proliferative Phase $(i)$ Breakdown of endometrium

$(b)$ Secretory Phase $(ii)$ Follicular phase

$(c)$ Menstruation $(iii)$ Luteal Phase

$A$ cell is connected between the points $A$ and $C$ of a circular conductor $ABCD$ of centre $O$ with angle $AOC = 60^{\circ}$. If $B_1$ and $B_2$ are the magnitudes of the magnetic fields at $O$ due to the currents in $ABC$ and $ADC$ respectively,the ratio $\frac{B_1}{B_2}$ is

$A$ string of mass $m$ and length $l$ hangs from the ceiling as shown in the figure. $A$ wave in the string moves upward. $v_A$ and $v_B$ are the speeds of the wave at points $A$ and $B$ respectively. Then $v_B$ is

Which of the following is the correct electronic configuration of $Cr$ $(Z=24)$?

Guttation is the result of

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