Question 203: Dual Nature of Matter and Radiation

Question

A particle A of mass 'm' and charge 'q' is accelerated by a potential difference of 50 V. Another particle B of mass ' 4 m' and charge 'q' is accelerated by a potential difference of 2500 V. The ratio of de-Broglie wavelengths $${{{\lambda _A}} \over {{\lambda _B}}}$$ is close to :

Accepted Answer

K.E. acquired by charge = K = qV
$$\lambda $$ = $${h \over P}$$ = $${h \over {\sqrt {2mK} }}$$ = $${h \over {\sqrt {2mqV} }}$$
$$ 	herefore $$  $${{{\lambda _A}} \over {{\lambda _B}}} = {{\sqrt {2m{}_B{q_B}{V_B}} } \over {\sqrt {2m{}_A{q_A}{V_A}} }} = \sqrt {{{4m.q.2500} \over {m.q.50}}}  = 2\sqrt {50} $$
$$ = 2 	imes 7.07 = 14.14$$

Answer

4.47

Answer

10.00

Answer

14.14

Answer

0.07

Dual Nature of Matter and Radiation

A particle A of mass 'm' and charge 'q' is accelerated by a potential difference of 50 V. Another particle B of mass ' 4 m' and charge 'q' is accelerated by a potential difference of 2500 V. The ratio of de-Broglie wavelengths ${{{\lambda _A}} \over {{\lambda _B}}}$ is close to :

Choose the correct answer: