A particle with the speed of 2.1 x 107 ms-1, its de Broglie wavelength is 6.5 x10-14 m. What is the mass of the particle

To find the mass of the particle, we can use the de Broglie wavelength equation:

λ = h / p

Where λ is the de Broglie wavelength, h is the Planck's constant (6.626 x 10^-34 Js), and p is the momentum of the particle.

Given that the de Broglie wavelength is 6.5 x 10^-14 m, we can rearrange the equation to solve for the momentum:

p = h / λ

Substituting the values, we have:

p = (6.626 x 10^-34 Js) / (6.5 x 10^-14 m)

Calculating this, we find:

p ≈ 1.018 x 10^-20 kg·m/s

Now, we can use the definition of momentum to find the mass of the particle:

p = mv

Where m is the mass of the particle and v is its velocity.

Given that the velocity of the particle is 2.1 x 10^7 m/s, we can rearrange the equation to solve for the mass:

m = p / v

Substituting the values, we have:

m = (1.018 x 10^-20 kg·m/s) / (2.1 x 10^7 m/s)

Calculating this, we find:

m ≈ 4.847 x 10^-28 kg

Therefore, the mass of the particle is approximately 4.847 x 10^-28 kg.