Answer:
approximately 6.49x10^-12 meters.
Step-by-step explanation:
To determine the wavelength of an alpha particle with a kinetic energy of 8.0x10^-13 J, we can use the de Broglie wavelength equation:
wavelength = h / p
where h is Planck's constant and p is the momentum of the particle.
To find the momentum of the alpha particle, we can use the equation:
p = sqrt(2mK)
where m is the mass of the alpha particle, K is its kinetic energy, and sqrt represents the square root.
The mass of an alpha particle is approximately 6.64x10^-27 kg. Substituting the given values, we get:
p = sqrt(2 x 6.64x10^-27 kg x 8.0x10^-13 J) ≈ 1.02x10^-19 kg m/s
Now we can substitute the values of h and p into the de Broglie wavelength equation to get:
wavelength = h / p = 6.626x10^-34 J s / 1.02x10^-19 kg m/s ≈ 6.49x10^-12 m
Therefore, the wavelength of an alpha particle with a kinetic energy of 8.0x10^-13 J is approximately 6.49x10^-12 meters.