A hydrogen atom moving at speed v collides with another hydrogen atom kept at rest. Find the minimum value of v for which one of the atoms may get ionized. The mass of a hydrogen atom = 1.67 × 10–27 kg.

According to problem this is a type of collision so we can conserve momentum and energy.


Let take v1 and v2 be two velocity of hydrogen after collision.


From conservation of momentum we have




From conservation of energy


+E


Where E is ionization energy and is equal to 13.6eV.


Solving this equation



Putting value of




And we know that



Substituting from above expressions.



Now for minimum v,


Then




m/s


m/s


1