1.

Find the recoil speed of a hydrogen atom after it emits a photon in going from n= 5 state to n= 1 state (R= 1.097 xx 10^7 m^(-1)):

Answer»

`2.4 ms^(-1)`
`4.18 ms^(-1)`
`3.2 ms^(-1)`
`6.4 ms^(-1)`

Solution :`1/lambda=R [1/n_(1)^(1)-1/n_(2)^(2)]`
`1/lambda=1.097 xx 10^(7) [1/1^(2)-1/5^(2)]`
`=1.097 xx 10^(7) xx (24)/(25) m^(-1)`
As EXTERNAL force is zero, so linear momentum remains constant i.e.
`P_("ATOM")+P_("photon")=0`
`P_("atom")=-P_("Photon")=-h/lambda`
`mv=-h/lambda, v=-(h)/(m lambda)=(-h)/(m). 1/lambda`
`rArr v=(6.63 xx 10^(-34))/(1.67 xx 10^(-27))xx 1.097 xx 10^(7) xx (24)/(25)`
`=4.18mm`


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