Question

The diffraction of radiation can be used to determine the spacing between atoms. In practice, the wavelength of the radiation used should be restricted to a value which is of the same order of magnitude as the interatomic distances to be determined. Such experiments are commonly performed using X-rays (electromagnetic radiation), however a beam of subatomic particles, such as of neutrons or electrons, may also be used if their corresponding de Broglie wavelength is of the appropriate magnitude.

Calculate the de Broglie wavelength of a neutron (m_n = 1.67493×10^-27 kg) moving at one eight thousandth of the speed of light (c/8000). For this question, ans is 1.056×10¹ pm, but please help me with next question.

Calculate the velocity of an electron (m_e = 9.10939×10^-31 kg) having a de Broglie wavelength of 188.8 pm.(help this one)

Answer 1

mass of the neutron m_n = 1.67493 x 10^-27 kg

speed v = c/8000 = 3 x 10⁸/8000 = 0.375 x 10⁵ m/s

plancks constant h = 6.62 x 10^-34 js

de Broglies wavelength = h / mv =  6.62 x 10^-34 / 1.67493 x 10^-27 x 0.375 x 10⁵

= 10.54 x 10^-12m

= 1.054 x 10¹ pm

b) mass of electron m = 9.10939 x 10^-31 Kg

  de Broglies wavelength = 188.8 x 10^-12 m

de Broglies wavelength = h/mv

velocity v =h/m

= 6.62 x 10^-34 / 9.10939 x 10^-31 x  188.8 x 10^-12

⁼ 0.00385 x 10⁹ m/s

= 3.85 x 10⁶ m/s