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 a 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.
7.99 e-14
To calculate the wavelength of a proton, we can use the de Broglie wavelength formula. The formula is given as:
λ = h / (m * v)
where λ is the wavelength, h is Planck's constant, m is the mass of the proton, and v is the velocity of the proton.
Given data:
h = 6.63 x 10^-34 J*s (Planck's constant)
m = 1.66 x 10^-27 kg (mass of a proton)
v = 5.00 x 10^6 m/s (speed of the proton)
Now, let's substitute the given data into the formula:
λ = (6.63 x 10^-34 J*s) / (1.66 x 10^-27 kg * 5.00 x 10^6 m/s)
First, multiply the denominator:
λ = (6.63 x 10^-34 J*s) / (8.3 x 10^-21 kg*m/s)
To divide by a fraction, we multiply by its reciprocal:
λ = (6.63 x 10^-34 J*s) * (1 / (8.3 x 10^-21 kg*m/s))
Next, multiply the numerator:
λ = (6.63 / 8.3) * (10^-34 J * s / kg * m/s)
Now, divide the values outside the parentheses:
λ = 0.7976 * (10^-34 J * s / kg * m/s)
Finally, convert the units:
λ = 0.7976 * 10^-34 J * s / (1.66 * 10^-27 kg * m/s)
λ ≈ 4.81 x 10^-8 m
Therefore, the wavelength of a proton with a speed of 5.00 x 10^6 m/s is approximately 4.81 x 10^-8 meters.