Question

A neutron having a mass of 1.67 x 10^-27 kg and moving at 10⁸ m/sec collides with a deuteron at rest and sticks to it. If mass of deuteron is 3.34 x 10^-27 kg, find the speed of combination –
1. \(0.333 \times {10^6}m/sec\)
2. \(0.333 \times {10^8}m/sec\;\)
3. \(0.333 \times {10^7}m/sec\)
4. None

Answer 1

Correct Answer - Option 2 : \(0.333 \times {10^8}m/sec\;\)

For neutron, \({m_1} = 1.67 \times {10^{ - 27}}kg\;and\;{u_1} = {10^8}m/sec\)

For deuteron, \({m_2} = 3.34 \times {10^{ - 27}}kg\;and\;{u_2} = 0\)

Let v be speed of combination, then by conservation of momentum –

\({m_1}{u_1} + {m_2}{u_2} = \left( {{m_1} + {m_2}} \right)v\)

\(\Rightarrow v = \frac{{1.67 \times {{10}^{ - 27}} \times {{10}^8} + 3.34 \times {{10}^{ - 27}} \times 0}}{{\left( {1.67 \times {{10}^{ - 27}} + 3.34 \times {{10}^{ - 27}}} \right)}} = 0.333 \times {10^8}m/sec\;\)