Final answer:
The wavelength of an electron traveling at 8.10 x 10^6 m/s is approximately 9.87 x 10^-11 m.
Step-by-step explanation:
To calculate the wavelength (λ) of an electron, we can use the de Broglie equation: λ = h / p, where h is Planck's constant and p is the momentum of the electron. The momentum of an object can be calculated as p = m * v, where m is the mass of the electron and v is its velocity.
Given that the velocity of the electron is 8.10 x 10^6 m/s and the mass of the electron is 9.11 x 10^-31 kg, we can calculate its momentum. Then, using the de Broglie equation, we can find the wavelength.
Let's calculate:
m = 9.11 x 10^-31 kg
v = 8.10 x 10^6 m/s
p = m * v = (9.11 x 10^-31 kg) * (8.10 x 10^6 m/s)
Now, we can use the momentum to calculate the wavelength:
λ = h / p = (6.63 x 10^-34 J*s) / ((9.11 x 10^-31 kg) * (8.10 x 10^6 m/s))
Simplifying the expression, we find:
λ = 9.87 x 10^-11 m
Therefore, the wavelength (in meters) of the electron traveling at 8.10 x 10^6 m/s is approximately 9.87 x 10^-11 m. So, the correct answer is D. 9.87 x 10^-11 m.