MCQ
Electrons are accelerated through a potential difference $V$ and protons are accelerated through a potential difference $4\, V$. The de-Broglie wavelengths are $\lambda_e $ and $\lambda_p $ for electrons and protons respectively. The ratio of $\frac{{{\lambda _e}}}{{{\lambda _p}}}$ is given by : (given $m_e$ is mass of electron and $m_p$ is mass of proton).
  • A
    $\frac{{{\lambda _e}}}{{{\lambda _p}}} = \sqrt {\frac{{{m_p}}}{{{m_e}}}} $
  • B
    $\frac{{{\lambda _e}}}{{{\lambda _p}}} = \sqrt {\frac{{{m_e}}}{{{m_p}}}} $
  • C
    $\frac{{{\lambda _e}}}{{{\lambda _p}}} = \frac{1}{2}\sqrt {\frac{{{m_e}}}{{{m_p}}}} $
  • $\frac{{{\lambda _e}}}{{{\lambda _p}}} = 2\sqrt {\frac{{{m_p}}}{{{m_e}}}} $

Answer

Correct option: D.
$\frac{{{\lambda _e}}}{{{\lambda _p}}} = 2\sqrt {\frac{{{m_p}}}{{{m_e}}}} $
d
Energy in joule $(E)$

$=$ charge $\times$ potential diff. in volt

${{\text{E}}_{{\text{electron }}}} = {q_{\text{e}}}{\text{V}}$ and ${{\text{E}}_{{\text{proton }}}} = {q_{\text{p}}}4{\text{V}}$

de-Broglie wavelength

$\lambda=\frac{\mathrm{h}}{\mathrm{P}}=\frac{\mathrm{h}}{\sqrt{2 \mathrm{mE}}}$

$\lambda_{\mathrm{c}}=\frac{\mathrm{h}}{\sqrt{2 \mathrm{m}_{\mathrm{e}} \mathrm{e} \mathrm{V}}}$ and $\lambda_{\mathrm{P}}=\frac{\mathrm{h}}{\sqrt{2 \mathrm{m}_{\mathrm{p}} \mathrm{e} 4 \mathrm{V}}}$

${\text{(}}\because {q_c} = {q_p}{\text{)}}$

$\therefore \frac{{{\lambda _{\text{c}}}}}{{{\lambda _{\text{P}}}}} = \frac{{\frac{{\text{h}}}{{\sqrt {2{{\text{m}}_{\text{e}}}{\text{eV}}} }}}}{{\frac{{\text{h}}}{{\sqrt {2{{\text{m}}_p}{\text{e4V}}} }}}}$ $ = \sqrt {\frac{{2{{\text{m}}_p}{\text{e4V}}}}{{2{{\text{m}}_e}{\text{eV}}}}} $

$ = 2\sqrt {\frac{{{{\text{m}}_{\text{p}}}}}{{{{\text{m}}_{\text{e}}}}}} $

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Similar questions

A bullet of mass $m$ and speed $v$ hits a pendulum bob of mass $M$ at time $t_1$, and passes completelythrough the bob. The bullet emerges at time $t_2$ with a speed of $v/2$. The pendulum bob is suspended by a stiff rod of length $l$ and negligible mass. After the collision, the bob can barely swing through a complete vertical circle.At time $t_3$, the bob reaches the highest position.What quantities are conserved in this process?
Match List$-I$ with List$-II$ 

List$-I$   List$-II$
$(A)$ $AC$ generator $(I)$ Detects the presence of current in the circuit
$(B)$ Galvanometer $(II)$ Converts mechanical energy into electrical energy
$(C)$ Transformer $(III)$ Works on the principle of resonance in $AC$ circuit
$(D)$ Metal detector $(IV)$ Changes an alternating voltage for smaller or greater value

Choose the correct answer from the options given below

Four $NOR$ gates are connected as shown in figure.

The truth table for the given figure is :

A car moves for half of its time at $80\, km/h$ and for rest half of time at $40\, km/h$. Total distance covered is $60 \,km$. What is the average speed of the car.........$km/h$
A candle flame of $3\, cm$ is placed at $3\, m$ from a wall. A concave mirror is kept at distance $x$ from the wall in such a way that image of the flame on the wall is $9\, cm$. Then $x$ is......$cm$
When Ultraviolet radiation of a certain frequency falls on a potassium target, the photo electrons released can be stopped completely by a retarding potential of $0.6 \,V$. If the frequency of the radiation is increased by $10 \%$, this stopping potential rises to $0.9 \,V$. The work function of potassium is ........ $eV$
A uniform magnetic field of induction $B$ is confined to a cylindrical region of radius $R$. The magnetic field is increasing at a constant rate of $\frac{{dB}}{{dt}} (tesla/second)$. An electron is placed at the point $P$ on the periphery of the field experiences an acceleration
Which of the following is wrong statement
For a transverse wave travelling along a straight line, the distance between two peaks (crests) is $5 \,m ,$ while the distance between one crest and one trough is $1.5 \,m$ The possible wavelengths (in $m$ ) of the waves are
A liquid disturbed by stirring comes to rest after some time due to its property of