Question:
CO$^{-}$ ion moving with kinetic energy of 20 keV dissociates into O$^{-}$ and C which move along the parent ion direction. Assuming no energy is released during dissociation, the kinetic energies of the daughters $(K.E.)_{O^-}$ and $(K.E.)_C$ are related as}
CO$^{-}$ ion moving with kinetic energy of 20 keV dissociates into O$^{-}$ and C which move along the parent ion direction. Assuming no energy is released during dissociation, the kinetic energies of the daughters $(K.E.)_{O^-}$ and $(K.E.)_C$ are related as}
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For equal momentum, KE $\propto \frac{1}{m}$.
Updated On: May 1, 2026
- $(K.E.)_{O^-} = (K.E.)_C$
- $(K.E.)_{O^-}/(K.E.)_C = 16/12$
- $(K.E.)_{O^-}/(K.E.)_C = 12/16$
- $(K.E.)_{O^-}/(K.E.)_C = 16/28$
- $(K.E.)_{O^-}/(K.E.)_C = 28/16$
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The Correct Option is C
Solution and Explanation
Concept:
Momentum conservation: \[ p = mv \] For same direction breakup, momentum is conserved and kinetic energy depends inversely on mass: \[ K = \frac{p^2}{2m} \Rightarrow K \propto \frac{1}{m} \]
Step 1: Masses.
\[ m_O = 16,\quad m_C = 12 \]
Step 2: Energy ratio.
\[ \frac{K_{O^-}}{K_C} = \frac{m_C}{m_O} = \frac{12}{16} \]
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