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7th_IPhO_1974

# 7th_IPhO_1974 - Problems of the 7th International Physics...

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( m - mass of electron; e - electric charge of electron; - Planck constant; numerical values of these quantities are not necessary.) Solution According to the Bohr model the energy levels of the hydrogen atom are given by the formula: 2 n E E i n - = , where n = 1, 2, 3, … The ground state corresponds to 1 = n , while the lowest excited state corresponds to 2 = n . Thus, the smallest energy necessary for excitation of the hydrogen atom is: i i E E E E E 4 3 4 1 1 2 ) 1 ( = - = - = . During an inelastic collision a part of kinetic energy of the colliding particles is converted into their internal energy. The internal energy of the system of two hydrogen atoms considered in the problem cannot be changed by less than E . It means that if the kinetic energy of the colliding atoms with respect to their center of mass is less than E , then the collision must be an elastic one. The value of 0 v can be found by considering the critical case, when the kinetic energy of the colliding atoms is equal to the smallest energy of excitation.
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7th_IPhO_1974 - Problems of the 7th International Physics...

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