Question 144: Dual Nature of Matter and Radiation

Question

An $$\alpha$$ particle and a carbon 12 atom has same kinetic energy K. The ratio of their de-Broglie wavelengths $$({\lambda _\alpha }:{\lambda _{C12}})$$ is :

Accepted Answer

$${K_\alpha } = {K_C}$$
$${{p_\alpha ^2} \over {2{m_\alpha }}} = {{p_C^2} \over {2{m_C}}}$$
$${{{p_\alpha }} \over {{p_C}}} = \sqrt {{{{m_\alpha }} \over {{m_C}}}} $$
So $${{{\lambda _\alpha }} \over {{\lambda _C}}} = {{h/{p_\alpha }} \over {h/{p_C}}} = \sqrt {{{{m_C}} \over {{m_\alpha }}}} $$
So $${{{\lambda _\alpha }} \over {{\lambda _C}}} = \sqrt 3 $$

Answer

$$1:\sqrt 3 $$

Answer

$$\sqrt 3 :1$$

Answer

$$3:1$$

Answer

$$2:\sqrt 3 $$

Dual Nature of Matter and Radiation

An $\alpha particle and a carbon 12 atom has same kinetic energy K. The ratio of their de-Broglie wavelengths ({\lambda _\alpha }:{\lambda _{C12}})$ is :

Choose the correct answer: