Calculate the linear momentum of photon of wavelength 750nm. What speed does an electron need to travel to have the same linear momentum.
To calculate the linear momentum of a photon, you can use the following equation:
Momentum (p) = Planck's constant (h) / wavelength (λ)
Given the wavelength of the photon is 750 nm, we need to convert it into meters by dividing by 1 billion:
wavelength (λ) = 750 nm / 1,000,000,000 = 7.5 × 10^-7 meters
Now, we can substitute the values into the equation:
Momentum (p) = h / λ = 6.626 × 10^-34 J·s / 7.5 × 10^-7 meters
Calculating this gives us:
p ≈ 8.835 × 10^-28 kg·m/s
To determine the speed at which an electron needs to travel to have the same linear momentum, we'll use the equation for linear momentum:
p = mass (m) × velocity (v)
Rearranging the equation, we can solve for velocity (v):
v = p / m
The mass of an electron is approximately 9.11 × 10^-31 kilograms. Substituting this value and the momentum we calculated earlier into the equation:
v ≈ (8.835 × 10^-28 kg·m/s) / (9.11 × 10^-31 kg) ≈ 9.68 × 10^2 m/s
Therefore, the speed at which an electron needs to travel to have the same linear momentum is approximately 968 m/s.