Calculate the de Broglie wavelength (in pm) of a hydrogen atom traveling 450 m/s .
lamda = h/mv
wavlength(lambda) will be in meters, convert to pm.
To calculate the de Broglie wavelength of a particle, you can use the formula:
λ = h / p
where λ is the de Broglie wavelength, h is the Planck's constant (6.62607015 × 10^-34 m^2 kg / s), and p is the momentum of the particle.
To find the momentum (p) of a particle, you can use the formula:
p = m * v
where p is the momentum, m is the mass of the particle, and v is the velocity of the particle.
For a hydrogen atom, the mass (m) is approximately 1.67 × 10^-27 kg.
Plug in the values into the equations:
p = (1.67 × 10^-27 kg) * (450 m/s)
p = 7.515 × 10^-25 kg*m/s
Now, calculate the de Broglie wavelength using the momentum:
λ = (6.62607015 × 10^-34 m^2 kg / s) / (7.515 × 10^-25 kg*m/s)
λ ≈ 8.805 × 10^-10 m
To convert the de Broglie wavelength from meters to picometers, you can multiply by a conversion factor:
1 m = 1 × 10^12 pm
So, the de Broglie wavelength of a hydrogen atom traveling at 450 m/s is approximately 8.805 × 10^-10 m, which is equivalent to 880.5 pm (picometers).