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The Bohr model can also be used to predict an approximate radius for an atom. The equation for the radius rr of the hydrogen atom is:\newliner=h2kπme2r=\frac{h^{2}k}{\pi me^{2}}\newlinewhere\newlinem=＂ mass of electron ＂m=\text{＂ mass of electron ＂}\newlineA student suggests that, for a speed of 1.4×107 ms−11.4 \times10^{7}\,\text{ms}^{-1}, neutrons would have a wavelength similar to the radius of a hydrogen atom.\newlineDetermine whether the student is correct.\newline＂ mass of neutron ＂=1.67×10−27 kg\text{＂ mass of neutron ＂}=1.67 \times10^{-27}\,\text{kg}

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Q. The Bohr model can also be used to predict an approximate radius for an atom. The equation for the radius rr of the hydrogen atom is:\newliner=h2kπme2r=\frac{h^{2}k}{\pi me^{2}}\newlinewhere\newlinem=＂ mass of electron ＂m=\text{＂ mass of electron ＂}\newlineA student suggests that, for a speed of 1.4×107 ms−11.4 \times10^{7}\,\text{ms}^{-1}, neutrons would have a wavelength similar to the radius of a hydrogen atom.\newlineDetermine whether the student is correct.\newline＂ mass of neutron ＂=1.67×10−27 kg\text{＂ mass of neutron ＂}=1.67 \times10^{-27}\,\text{kg}
  1. Use formula for neutron: Use the de Broglie wavelength formula for the neutron: λ=hmv\lambda = \frac{h}{mv}, where hh is Planck's constant, mm is the mass of the neutron, and vv is the velocity of the neutron.
  2. Plug in values: Plug in the values: h=6.626×10−34h = 6.626 \times 10^{-34} J⋅\cdots (Planck's constant), m=1.67×10−27m = 1.67 \times 10^{-27} kg (mass of neutron), and v=1.4×107v = 1.4 \times 10^7 ms−1^{-1} (velocity of neutron).
  3. Calculate wavelength: Calculate the wavelength λ\lambda: λ=6.626×10−34 J⋅s1.67×10−27 kg×1.4×107 ms−1\lambda = \frac{6.626 \times 10^{-34} \text{ J}\cdot\text{s}}{1.67 \times 10^{-27} \text{ kg} \times 1.4 \times 10^7 \text{ ms}^{-1}}.
  4. Perform calculation: Perform the calculation: λ=6.626×10−341.67×10−27×1.4×107=2.82×10−10\lambda = \frac{6.626 \times 10^{-34}}{1.67 \times 10^{-27} \times 1.4 \times 10^7} = 2.82 \times 10^{-10} meters.
  5. Compare to hydrogen atom radius: Compare the calculated wavelength of the neutron to the known radius of the hydrogen atom, which is approximately 5.29×10−115.29 \times 10^{-11} meters.
  6. Conclusion: The wavelength of the neutron is much larger than the radius of the hydrogen atom, so the student's suggestion is incorrect.

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