A neutron with kinetic energy K collides head-on with a stationary hydrogen atom in its ground state. Assuming the mass of the neutron is equal to the mass of the hydrogen atom, the minimum value of K required for the hydrogen atom to subsequently emit a spectral line in the Balmer series is nearly :

Step-by-step solution

To emit a photon in the Balmer series, the electron in the hydrogen atom must fall to n=2 from a higher state. The minimum excited state required is n=3 . The energy required to excite the hydrogen atom from n=1 to n=3 is: E = 13.6 ( 1 - 1 3^2 ) = 13.6 8 9 = 12.09 eV In a collision between a moving particle of mass m and a stationary particle of mass m , the maximum kinetic energy that can be converted into internal energy (excitation) occurs in a perfectly inelastic collision. By conservation of momentum, the comm