Calculate the de Broglie wavelength (in pm ) of a hydrogen atom traveling 445 m/s.
To calculate the de Broglie wavelength, you can use the de Broglie equation, which is given by:
λ = h / p
Where λ is the de Broglie wavelength, h is the Planck's constant (h = 6.626 x 10^-34 Js), and p is the momentum of the particle.
To calculate the momentum (p) of a particle, you can use the equation:
p = m * v
Where m is the mass of the particle and v is its velocity.
In the case of a hydrogen atom, the mass (m) is approximately 1.67 x 10^-27 kg.
Using the given velocity of 445 m/s, we can now calculate the momentum:
p = (1.67 x 10^-27 kg) * (445 m/s)
p ≈ 7.42 x 10^-25 kg·m/s
Now, substitute the calculated momentum into the de Broglie equation to find the de Broglie wavelength:
λ = (6.626 x 10^-34 Js) / (7.42 x 10^-25 kg·m/s)
λ ≈ 8.92 x 10^-10 m
To convert the wavelength from meters to picometers (pm), multiply by a conversion factor:
1 m = 1 x 10^12 pm
Therefore,
λ = 8.92 x 10^-10 m * (1 x 10^12 pm/1 m)
λ ≈ 8.92 x 10^2 pm
So, the de Broglie wavelength of a hydrogen atom traveling at 445 m/s is approximately 892 pm.