Answer :
The wavelength of the matter wave for a 173kg astronaut can be calculated using the de Broglie wavelength formula, but the astronaut's speed must be given to compute the exact value. Without the speed, it's impossible to determine the wavelength.
To calculate the wavelength of the matter wave associated with a moving astronaut, we utilize the de Broglie wavelength formula, which relates the matter wave's wavelength (λ) to its momentum (p), given by λ = h / p, where h is Planck's constant (6.626 × 10-34 m2 kg / s). Knowing the astronaut's mass (m) is 173 kg and velocity (v) is given to be the same as in the question, we can find the momentum as p = mv. However, the exact speed is not provided, hence it cannot be calculated without that information.
If the speed were given, we could calculate the wavelength by substituting the values for m, v, and h into the de Broglie equation. It's important to note that since we are talking about an astronaut, the matter wave's wavelength will be incredibly small and practically unobservable due to the large mass and relatively small speeds involved compared to the speed of light.
