Final answer:
The mass of a particle traveling at 90% of the speed of light with a wavelength of 1.5 x 10^-15 meters can be calculated using the de Broglie equation, resulting in a mass of 1.63 x 10^-30 kg.
Step-by-step explanation:
To calculate the mass of a particle with a velocity that is 90% of the speed of light and a given wavelength, you can use the de Broglie wavelength formula λ = h/mv, where λ is the wavelength, h is Planck's constant, m is the mass of the particle, and v is the velocity of the particle. Knowing that the speed of light (c) is approximately 3.00 × 108 m/s, the particle's velocity (v) is 0.9c. Therefore, the velocity we'll use in the calculation is 2.70 × 108 m/s. With the wavelength (λ) given as 1.5 × 10-15 meters and Planck's constant (h) as 6.626 × 10-34 J·s, we can rearrange the equation to solve for the mass (m) of the particle.
Firstly, rearrange the de Broglie equation to solve for mass: m = h / (λv).
Substitute the known values into the equation:
m = æ.626 × 10-34 J·s / (1.5 × 10-15 m × 2.70 × 108 m/s) = 1.63 × 10-30 kg.