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After absorbing a slowly moving neutron of mass m_N (momentum ≈ 0) a nucleus of mass M breaks into two nuclei of masses m1 and 5m1 (6m1 = M + m_N), respectively. If the de Broglie wavelength of the nucleus with mass m1 is λ, the de Broglie wavelength of the nucleus with mass 5m1 is

1. 5λ
2. λ/5
3. λ
4. 25λ

Correct answer: λ

Solution

The de Broglie wavelength is inversely proportional to the momentum of an object. Since the total momentum before and after the neutron absorption is conserved and the neutron has negligible momentum, the two resulting nuclei will have wavelengths that depend on their masses. The nucleus with mass 5m1 has a greater mass, but since the momentum distribution remains balanced, both nuclei will end up having the same de Broglie wavelength, which is λ.

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