Q1 / 160 · AP EAMCET 2019 (22 Apr Shift 1) · Chemistry

If the kinetic energy of an electron of mass \(9.0 \times 10^{-31} \mathrm{~kg}\) is \(2.0 \times 10^{-25} \mathrm{~J}\), the wavelength of the electron in \(\mathrm{nm}\) is approximately

  • A
    1004.3
  • B
    1204.3
  • Correct answer
    C
    1104.3
  • D
    994.3

Solution

Given, Kinetic energy of an electron \(=2.0 \times 10^{-25} \mathrm{~J}\) Mass of electron \(=9.0 \times 10^{-31} \mathrm{~kg}\) Wavelength of the electron \(=\) ? \(\begin{aligned} \lambda & =\frac{h}{\sqrt{2 m(\mathrm{KE})}}\left(\text { here, } h=6.6 \times 10^{-34} \mathrm{Js}\right) \\ \lambda & =\frac{6.63 \times 10^{-34} \mathrm{Js}}{\sqrt{2 \times 9.0 \times 10^{-31} \mathrm{~kg} \times 2 \times 10^{-25} \mathrm{~J}}} \\ \lambda & =1.1043 \times 10^{-6} \mathrm{~m}=\frac{1.1043 \times 10^{-6}}{10^{-9}} \mathrm{~nm} \\ & =1104.3 \mathrm{~nm} \end{aligned}\)

Hence, the correct answer is option: 'C'.

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