What is the speed of an argon atom that has a de Broglie wavelength of 5.2 pm?
To calculate the speed of an argon atom with a given de Broglie wavelength, we can use the de Broglie wavelength formula:
λ = h / (m*v)
Where:
- λ is the de Broglie wavelength
- h is Planck's constant (6.626 x 10^-34 J·s)
- m is the mass of the particle
- v is the velocity
For an argon atom, the mass (m) can be found in the periodic table, which is approximately 6.63 x 10^-26 kg.
Now, let's rearrange the formula to solve for v:
v = h / (m * λ)
Substituting the given values:
v = (6.626 x 10^-34 J·s) / ((6.63 x 10^-26 kg) * (5.2 x 10^-12 m))
Calculating this expression will give you the speed of the argon atom.
To determine the speed of an argon atom with a given de Broglie wavelength, we can make use of the de Broglie wavelength equation:
λ = h / (mv)
Where:
λ is the de Broglie wavelength,
h is Planck's constant (6.626 x 10^-34 J·s),
m is the mass of the argon atom, and
v is the velocity/speed of the argon atom.
First, we need to convert the de Broglie wavelength from picometers (pm) to meters (m).
1 pm = 1 x 10^-12 m
So, the given de Broglie wavelength of 5.2 pm can be converted to meters as follows:
λ = 5.2 x 10^-12 m
Now, rearranging the de Broglie wavelength equation to solve for velocity:
v = h / (mλ)
Next, we need to find the mass of an argon atom. The atomic mass of argon (Ar) is approximately 39.95 atomic mass units (u).
1 atomic mass unit (u) = 1.66 x 10^-27 kg
So, the mass of an argon atom can be calculated as:
m = (39.95 u) x (1.66 x 10^-27 kg/u)
Now, substitute the values into the equation to calculate the speed:
v = (6.626 x 10^-34 J·s) / ([39.95 u] x [1.66 x 10^-27 kg/u]) x (5.2 x 10^-12 m)
By performing the calculations, you'll find the speed of the argon atom with a de Broglie wavelength of 5.2 pm.
wavelength = h/mv.
m is in kg
v in m/s
wavelength is in m