Estimate the wavelength (in nm) of such a proton moving at 2.81x10^8 m/s (mass of a proton = 1.673x10^-27 kg).
wavelength = h/mv
Solve for wavelength in meters and convert to nm.
how do you convert it into nm
1 m = 1E9 nm so multiply the wavelength you obtain in meters by 1E9.
is 1.4x10^-15 the correct answer ?
Your answer is in m. To convert to nm you multiply by 1E9. Also, you are allowed 3 significant figures (from the 2.81) and I obtained 1.405E-15 m so I would round that to 1.40E-15 m (to 3 s.f.) which converts to 1.40E-6 nm.
okay. thank you !!
To estimate the wavelength of a moving proton, you can use the de Broglie wavelength equation:
λ = h / p
where λ is the wavelength, h is the Planck's constant (h = 6.626 x 10^-34 J·s), and p is the momentum of the proton.
To find the momentum of the proton, you can use the equation:
p = m * v
where p is the momentum, m is the mass of the proton, and v is the velocity of the proton.
Let's plug in the given values:
m = 1.673 x 10^-27 kg
v = 2.81 x 10^8 m/s
Calculating the momentum:
p = (1.673 x 10^-27 kg) * (2.81 x 10^8 m/s)
p = 4.704 x 10^-19 kg·m/s
Now, we can calculate the wavelength using the de Broglie wavelength equation:
λ = (6.626 x 10^-34 J·s) / (4.704 x 10^-19 kg·m/s)
λ ≈ 1.407 x 10^-15 m
Finally, to convert the wavelength into nanometers (nm), you can multiply it by 10^9:
λ ≈ 1.407 x 10^-15 m * 10^9 nm/m
λ ≈ 1.407 nm
Therefore, the estimated wavelength of the proton moving at 2.81 x 10^8 m/s is approximately 1.407 nm.