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# A nucleus of uranium decays at rest into nuclei of thorium and helium. Then

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a
The helium nucleus has more momentum than the thorium nucleus.
b
The helium nucleus has less kinetic energy than the thorium nucleus.
c
The helium nucleus has more kinetic energy than the thorium nucleus.
d
The helium nucleus has less momentum than the thorium nucleus.

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detailed solution

Correct option is C

If p→Th and p→He  are the momenta of thorium and helium nuclei respectively, then according to law of conservation of linear momentum0=p→Th+p→He or p→Th=-p→He-ve sign shows that both are moving in opposite directions. But in magnitudepTh=pHeIf mTh and mHe are the masses of thorium and helium nuclei respectively, then Kinetic energy of thorium nucleus is KTh=pTh22mTh and that of helium nucleus is KHe=pHe22mHe∴  KThKHe=pThpHe2mHemTh But pTh =pHe and mHeKThThus the helium nucleus has more kinetic energy than the thorium nucleus.

In single slit diffraction pattern under bichromatic illumination. If the first minimum with the wavelength $\mathrm{\lambda }$1 is found to be coincident with third maximum of $\mathrm{\lambda }$2, then