QJEEM22Ph01ff: JEE Main 2022 Physics - Class 12 JEEM22Ph01ff Solution: An particle and a carbon 12 atom has same kinetic energy K. The …

${K_\alpha } = {K_C}$

${{p_\alpha ^2} \over {2{m_\alpha }}} = {{p_C^2} \over {2{m_C}}}$

${{{p_\alpha }} \over {{p_C}}} = \sqrt {{{{m_\alpha }} \over {{m_C}}}}$

So ${{{\lambda _\alpha }} \over {{\lambda _C}}} = {{h/{p_\alpha }} \over {h/{p_C}}} = \sqrt {{{{m_C}} \over {{m_\alpha }}}}$

So ${{{\lambda _\alpha }} \over {{\lambda _C}}} = \sqrt 3$