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Question
A radioactive nucleus decays by β emission. Both β and neutrino move mutually at right angle with momentum 6×10−21kgms−1 and 3×10−21kgms−1. The direction of recoil of nucleus with respect to electron is :
A radioactive nucleus decays by β emission. Both β and neutrino move mutually at right angle with momentum 6×10−21kgms−1 and 3×10−21kgms−1. The direction of recoil of nucleus with respect to electron is :
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Solution
The correct option is C 180−tan−1(12)
As the nucleus was at rest, its final momentum must equal the opposite of the vector sum of the electron & neutrino momenta,.which are at right anglesLet the electron direction be along the positive x-axis and neutrino be -y axis
magnitude of nucleus momentum is p=√62+32×10−21=√45×10−21kgms−1
direction is −tan−1(3×10−216×10−21)=−tan−1(12)
Therefore the recoil direction is opposite, which is 180−tan−1(12)
As the nucleus was at rest, its final momentum must equal the opposite of the vector sum of the electron & neutrino momenta,.which are at right angles
Let the electron direction be along the positive x-axis and neutrino be -y axis
magnitude of nucleus momentum is p=√62+32×10−21=√45×10−21kgms−1
direction is −tan−1(3×10−216×10−21)=−tan−1(12)
Therefore the recoil direction is opposite, which is 180−tan−1(12)
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