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Home / Doubts and Solutions/NEET/Physics

when a hydrogen atom emits a photon during thevtransition n=5 to n=1,its recoil speed is?

Asked by shanchipadhi143 10th September 2018, 9:47 AM
Answered by Expert
Answer:
We know that momentum is given by equation
 
p= h/λ
 
rightwards double arrow space m cross times v space equals space h over lambda rightwards double arrow v space equals space fraction numerator h over denominator m cross times lambda end fraction ....(1)
Hydrogen atom emits photon during transition from n= 5 to n=1 
rightwards double arrow space 1 over lambda space equals space R open parentheses 1 over n subscript 1 squared minus fraction numerator begin display style 1 end style over denominator begin display style n subscript 2 squared end style end fraction close parentheses R space minus space R y d b e r g apostrophe s space co n s tan t space equals 1.097 cross times 10 to the power of 7 m space to the power of negative 1 end exponent rightwards double arrow fraction numerator begin display style 1 end style over denominator begin display style lambda end style end fraction equals R open parentheses fraction numerator begin display style 1 end style over denominator begin display style 1 squared end style end fraction minus fraction numerator begin display style 1 end style over denominator begin display style 5 squared end style end fraction close parentheses rightwards double arrow lambda equals fraction numerator 25 over denominator 24 cross times 1.097 cross times 10 to the power of 7 end fraction space equals space 9.48 space cross times 10 to the power of negative 8 end exponent space m
Substituting in equation (1) we get
 
m a s s space o f space p r o t o n space equals space 1.6 space cross times 10 to the power of negative 27 end exponent space k g space rightwards double arrow v equals fraction numerator 6.62 space cross times space 10 to the power of negative 34 end exponent space m squared space k g divided by s space over denominator 1.6 space cross times 10 to the power of negative 27 end exponent space cross times space 9.48 space cross times 10 to the power of negative 8 space end exponent end fraction rightwards double arrow v equals space 4.36 space m divided by s space
 
This is the recoil speed of hydrogen atom. 
Answered by Expert 10th September 2018, 11:46 AM
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