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CBSE Class 12-science Answered

Please solve this .
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Asked by abhitailor158 | 23 Apr, 2020, 03:36: PM
answered-by-expert Expert Answer
A particle trapped in one dimensional box of dimension 10 Ao is shown in figure.
 
The particle is trapped in that box due to infinit potentila at x= 0 and at x=10 Ao , whereas inside box particle have zero potential .
 
Wave function Ψ of particle in one dimension box is given by
 
Ψn = (2/a)1/2 sin ( n π x / a ) .........................(1)
 
where n =1 for ground state , n =2 for first excited state and a is dimension of box , in this question a = 10 Ao
 
Probability p of finding the particle at centre in an interval of 1 Ao is given by
 
begin mathsize 14px style p space equals integral subscript 4.5 end subscript superscript 5.5 end superscript capital psi to the power of asterisk times capital psi space d x space equals space space 1 fifth integral subscript 4.5 end subscript superscript 5.5 end superscript sin squared open parentheses fraction numerator n pi x over denominator 10 end fraction close parentheses d x end style
In above equation we have substituted a = 10 Ao and all distances are expressed in terms of Ao
 
By performing above integration we get p = 1/10 independent of n , i.e. required probability is same for ground state as well as excited state



Answered by Thiyagarajan K | 24 Apr, 2020, 01:56: PM

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