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What is the wavelength of the matter wave associated with a 157 kg astronaut (including her spacesuit) moving at a certain speed?

Answer :

The wavelength astronaut astronaut of the matter wave associated with a 157 kg astronaut (including her spacesuit) moving at the same speed is approximately [tex]1.48 * 10^{-44}[/tex] meters.

To calculate the wavelength of the matter wave associated with a 157 kg astronaut moving at a certain speed, we need to use the de Broglie wavelength formula:

[tex]\lambda = \frac{h}{m * v}[/tex]

where:

λ is the wavelength

h is Planck's constant ([tex]6.626 * 10^{-34}[/tex] m² kg / s)

m is the mass of the astronaut (157 kg)

v is the speed of the astronaut

If the speed (v) of the astronaut is not given, we cannot compute an exact numerical value for the wavelength.

  • Assuming a hypothetical speed, say 95% the speed of light (c = [tex]3 * 10^{8}[/tex] m/s), this would be:

v = 0.95 * c = [tex]0.95 * 3 * 10^{8}[/tex] m/s = [tex]2.85 * 10^{8}[/tex] m/s

  • Using these values, the wavelength λ is calculated as:

[tex]\lambda = \frac{6.626 * 10^{-34}}{157 * 2.85 * 10^8}[/tex] ≈ [tex]1.48 * 10^{-44}[/tex] meters.

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