Uttarakhand PMT Uttarakhand PMT Solved Paper-2007

  • question_answer
    In hydrogen spectrum the wavelength of \[{{H}_{\alpha }}\] line is 656 nm, where as in the spectrum of a distant galaxy, \[{{H}_{\alpha }}\]line wavelength is 706 nm. Estimated speed of galaxy with respect to earth is

    A)  \[2\times {{10}^{8}}m/s\]   

    B)  \[2\times {{10}^{7}}m/s\]

    C)  \[2\times {{10}^{6}}m/s\]  

    D)  \[2\times {{10}^{5}}m/s\]

    Correct Answer: B

    Solution :

     \[\frac{\Delta \lambda }{\lambda }=\pm \frac{v}{c}\] Here,\[(-)\]sign to be used for approaching (+) sign to be used for receding \[\Rightarrow \] \[\frac{\Delta \lambda }{\lambda }=\frac{706-656}{656}=+\frac{v}{c}\] \[\Rightarrow \] \[\frac{v}{c}=\frac{50}{656}\] \[\Rightarrow \] \[v=\frac{50}{656}\times c\] \[\therefore \] \[v=\frac{50}{656}\times 3\times {{10}^{8}}\] \[=2\times {{10}^{7}}m/s\]


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