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
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From conservation of energy
+E
Where E is ionization energy and is equal to 13.6eV.
Solving this equation
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Putting value of ![]()
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And we know that
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Substituting
from above expressions.
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Now for minimum v, ![]()
Then
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m/s
m/s