An H -atom moving with speed v makes a head-on collision with another H -atom at rest. Both the atoms are in the ground state. The minimum value of velocity v for which one of the atoms may excite is

Step-by-step solution

For v m i n collision should be completely inelastic. According to energy conservation principle, ∴ 1 2 m v m i n 2 = 1 2 m v 2 + 1 2 m v 2 + ∆ E ...(i)) According to momentum conservation principle. m v m i n = m v + m v ∴ v = m m i n 2 ...(ii) After solving eq. (i) an d(ii), we get 1 2 m v m i n 2 = 2 ∆ E ∴ v m i n = 4 ∆ E m Here, ∆ E = minimum excitation energy = 10.2 e V m = 1.67 × 10 - 27 k g ∴ v m i n = 4 × 10.2 × 1.6 × 10 - 19 1.67 × 10 - 27 = 6.25 × 10 4   m   s - 1