Using Planck's constant as h=6.63 E-34 J*s, what is the wavelength of a proton with a speed of 5.00 E6 m/s? The mass of the proton is 1.66 E-27 kg. Remember to identify your data, show your work, and report the answer using the correct number of significant digits and units.
m=1.66 v=5.00 h=6.63
(6.63)/ (1.66 x 5.00) = 6.63/8.3=0.79
My answer is 0.79 E-34 m. Is this correct?
Your approach is correct, but you need to calculate the wavelength using the de Broglie wavelength formula. You have identified the mass (m) and speed (v) of the proton, and the Planck's constant (h). Now, you can find the wavelength using the formula:
λ = h / (m * v)
You have correctly set up the calculation, but you haven't carried out the correct multiplication in the denominator.
λ = (6.63 E-34) / (1.66 E-27 * 5.00 E6)
λ = (6.63 E-34) / (8.30 E-21)
To carry out this calculation, divide:
λ = 7.98 E-14 m
So, the correct answer is 7.98 E-14 m.
To calculate the wavelength of a proton with a given speed, you can use the de Broglie wavelength formula, which relates the wavelength of a particle to its momentum. The formula is:
λ = h / p
where λ is the wavelength, h is Planck's constant, and p is the momentum of the particle.
Given:
h = 6.63 x 10^(-34) J*s (Planck's constant)
v = 5.00 x 10^6 m/s (speed of the proton)
m = 1.66 x 10^(-27) kg (mass of the proton)
First, we need to calculate the momentum of the proton, which is given by the formula:
p = m * v
Substituting the given values into the formula:
p = (1.66 x 10^(-27) kg) * (5.00 x 10^6 m/s)
p = 8.30 x 10^(-21) kg*m/s
Now, we can calculate the wavelength using the de Broglie formula:
λ = h / p
Substituting the values:
λ = (6.63 x 10^(-34) J*s) / (8.30 x 10^(-21) kg*m/s)
λ = 0.797 x 10^(-13) m
λ = 7.97 x 10^(-15) m
The final answer should be reported with the correct number of significant digits and units. Since the given speed was provided with 3 significant digits, we should report the answer with 3 significant digits as well:
λ = 7.97 x 10^(-15) m