Final answer:
The de Broglie wavelength of an electron shot straight up with a speed of 150 m/s is calculated using the de Broglie equation, which yields a wavelength of 4.85 micrometers.
Step-by-step explanation:
The student's question pertains to calculating the de Broglie wavelength of an electron when it reaches a height of 500 m, with a given initial speed. To find the wavelength of the electron, we use the de Broglie equation, λ = h/mv, where λ is the wavelength, h is Planck's constant (6.626 x 10-34 J·s), m is the mass of the electron (9.11 x 10-31 kg), and v is the velocity of the electron.
Since the question asks for the wavelength at a certain height, assuming no forces other than gravity act on the electron, its speed will decrease due to potential energy increase. However, the question specifies to calculate the wavelength with the initial speed. Thus, we take v to be 150 m/s. Now we substitute the known values into the equation to find the wavelength.
λ = h / (m * v) = (6.626 x 10-34 J·s) / (9.11 x 10-31 kg * 150 m/s) = 4.85 x 10-6 m, or 4.85 micrometers.