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JEE Main 20198 AprilEvening Shift

Exam: JEE Main
Year: 2019
Date: 8 April
Shift: Evening Shift
Subject: Physics
Chapter: Dual Nature of Matter

JEE Main 2019 · 8 April · Evening Shift · Physics · Dual Nature of Matter

A nucleus A, with a finite de-broglie wavelength λ _ A , undergoes...

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:

Options

A ${\lambda}_{A}, \dfrac{{\lambda}_{A}}{2}$
B $\dfrac{{\lambda}_{A}}{2}, {\lambda}_{A}$
C ${\lambda}_{A}, 2{\lambda}_{A}$
D $2{\lambda}_{A}, {\lambda}_{A}$

Correct answer

B. $\dfrac{{\lambda}_{A}}{2}, {\lambda}_{A}$

Step-by-step solution

\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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