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Dual Nature of Matter

JEE Main level, single correct, medium

72 of 200

Question 72 of 200

A nucleus $A,$ with a finite de-broglie wavelength ${\lambda }_{A},$ undergoes spontaneous fission into two nuclei $B$ and $C$ of equal mass. $B$ flies in the same direction as that of $A,$ while $C$ flies in the opposite direction with a velocity equal to half of that of $B.$ The de-Broglie wavelengths ${\lambda }_{B}$ and ${\lambda }_{C}$ of B and C are respectively:

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Answer: (B) $\dfrac{{\lambda }_{A}}{2},{\lambda }_{A}$

\dfrac{h}{{\lambda }_{A}}=\dfrac{h}{{\lambda }_{B}}-\dfrac{h}{{\lambda }_{C}}

…(i)
Also

{\lambda }_{C}=2{\lambda }_{B}

...(ii)
From equation (i) & (ii),

\dfrac{1}{{\lambda }_{A}}=\dfrac{1}{{\lambda }_{B}}-\dfrac{1}{2{\lambda }_{B}}

{\lambda }_{B}=\dfrac{{\lambda }_{A}}{2}; {\lambda }_{C}={\lambda }_{A}

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JEE Main 2025 Apr 2 Shift 1 question paper

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