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A moving hydrogen atom makes a head-on c...

A moving hydrogen atom makes a head-on collision with a stationary hydrogen atom. Before collision, both atoms are in ground state and after collision they move together . What is the minimum KE of an atom, such that one of the atoms reaches one of the excitation state.

A

`20.4 e V`

B

`25.4 e V`

C

`2 e V`

D

`204 e V`

Text Solution

Verified by Experts

The correct Answer is:
A
Let `K` be the kinetic energy of the moving hydrogen atom `K`' the kinetic energy of combined mass after collision.
From conservation of liner momentum .
`p = p' implies sqrt (2 K m) = sqrt(2 K' (2 m))`
or `K = 2K'`
From conservation of energy
`K = K' + Delta E`
Solving Eqs. (i) and (ii), we get `Delta E = (K)/(2)`
Now, minimum value of `Delta E` for hydrogen atom is `10.2 e V`.
or `Delta E ge 10.2 e V`
`:. (K)/(2) ge 10.2 e V`
`:. K ge 20.4 e V`

Therefore, the minimum kinetic energy of moving hydrogen is `20.4 e V`
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