Can someone please help me? Compare the wavelength of the Hydrogen electron havi

Question

Can someone please help me?

Compare the wavelength of the Hydrogen electron having a speed equivalent to 1% of the speed of light to its confinement space. Do the same for a student of about 70 kg entering a classroom at a speed of 6 km/h. What can you conclude from these two calculations? Determine the uncertainty on the speed of the electron in the H atom knowing the uncertainty on position is Bohr radius (a_0 = 0.529 10^-10m). Then, determine the uncertainty on the speed of a grain of dust of mass m equal to 10^-6 g and localized with 10^-6 m precision. What can you conclude from these two calculations? A wavefunction Psi (r, t) is a complex function that presents a complete description of a particle of mass m at time t Does this wavefunction have a unit?

Explanation / Answer

1) As per de Broglie's Equation ; wavelength = Planck's constant/{mass*velocity)

Planck's constant = 6.63*10-34 J-s ; m = 9.1*10-31 kg ; v = 3*105 m/s (1% of speed of light)

Thus, wavelength = 2.428*10-9 m = 2.428 nm

wavelength of student = (6.63*10-34)/(70*16.67) = 5.682*10-37 m

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