Haryana PMT Haryana PMT Solved Paper-2009

  • question_answer
    According to Bohrs theory of hydrogen atom, for the electron in the \[{{n}^{th}}\] allowed orbit the (i) linear momentum is proportional to 1/\[n\] (ii) radius is proportional to \[n\] (iii) kinetic energy is proportional to 1/\[n\]2 (iv) angular momentum is proportional to \[n\] Choose the correct option from the codes given below:

    A)  (i), (iii), (iv)                        

    B)  (i)

    C)  (i), (ii)                                  

    D)  (iii)

    Correct Answer: A

    Solution :

                    According to Bohrs theory of hydrogen atom, angular momentum is quantized ie, \[L=m{{v}_{n}}{{r}_{n}}=n\left( \frac{h}{2\pi } \right)\]  or \[L\propto n\] Radius of the orbit \[{{r}_{n}}\propto \frac{{{n}^{2}}}{Z}\] Kinetic energy \[=\frac{k{{Z}^{2}}{{e}^{2}}}{2{{n}^{2}}}\]ie, \[k\propto \frac{1}{{{n}^{2}}}\]and linear momentum is proportional to 1/n.


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