NEET Sample Paper NEET Sample Test Paper-15

  • question_answer The de Broglie wavelength of an electron moving with a velocity \[1.5\times {{10}^{8}}m\,{{s}^{-1}}\]is equal to that of a photon. The ratio of the kinetic energy of the electron to that of the photon is

    A)  2                                

    B)  4

    C)  \[\frac{1}{2}\]                                   

    D)  \[\frac{1}{4}\]

    Correct Answer: D

    Solution :

    The speed of photon\[=c=3\times {{10}^{8}}\,m/s,\] Wavelength of photon is v. Wavelength of electron \[=\frac{h}{mv}.\] Now, \[\frac{\text{KE}\,\text{of}\,\text{electron}}{\text{KE}\,\text{of}\,\text{photon}}=\frac{\frac{1}{2}m{{v}^{2}}}{hv}=\frac{1}{2}\frac{m{{v}^{2}}}{hc}\lambda =\frac{m{{v}^{2}}h}{2hcmv}\] \[=\frac{v}{2c}=\frac{1}{4}\,(\because \,v=c/2)\] Hence, the correction option is [d].

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