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?
To calculate the wavelength of a proton with a given speed using Planck's constant, you can use the de Broglie wavelength equation, which relates the wavelength of a particle to its momentum:
λ = h / p
where λ is the wavelength, h is Planck's constant, and p is the momentum of the particle.
To find the momentum of the proton, you can use the following equation:
p = m * v
where p is the momentum, m is the mass of the proton, and v is its speed.
Now, let's insert the given values into the equations:
m = 1.66 E-27 kg
v = 5.00 E6 m/s
h = 6.63 E-34 J*s
First, calculate the momentum:
p = m * v = (1.66 E-27 kg) * (5.00 E6 m/s) = 8.3 E-21 kg·m/s
Now, substitute the derived momentum into the wavelength equation:
λ = h / p = (6.63 E-34 J*s) / (8.3 E-21 kg·m/s)
To divide these numbers in scientific notation, you subtract the exponents:
λ = (6.63 / 8.3) E-34-(-21) = 0.797590361 E-13 = 7.98 E-14 m
Therefore, the wavelength of a proton with a speed of 5.00 E6 m/s is approximately 7.98 E-14 meters.
Note: I rounded the answer to the correct number of significant digits (3) and included the correct unit (m).
To calculate the wavelength of a proton, we can use the de Broglie wavelength equation:
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 speed of the proton.
Given:
h = 6.63 x 10^(-34) J·s
m = 1.66 x 10^(-27) kg
v = 5.00 x 10^(6) m/s
Substituting these values into the equation, we get:
λ = (6.63 x 10^(-34) J·s) / [(1.66 x 10^(-27) kg) * (5.00 x 10^(6) m/s)]
Calculating the numerator:
6.63 x 10^(-34) J·s = (6.63 / 1) x 10^(-34) J·s = 6.63 x 10^(-34) J·s
Calculating the denominator:
(1.66 x 10^(-27) kg) * (5.00 x 10^(6) m/s) = (1.66 x 5.00) x (10^(-27) kg * m/s)
= 8.30 x 10^(-27) kg·m/s
Substituting the values back into the equation:
λ = (6.63 x 10^(-34) J·s) / (8.30 x 10^(-27) kg·m/s)
Dividing the two values:
= 7.97590361 x 10^(-8) m
Rounding the answer to the correct number of significant digits and using scientific notation, the wavelength of the proton is approximately 7.98 x 10^(-8) m.
Your work makes no sense to me
What you have, I think, is that
planck'sconstant=wavelength*mass*velocity
Where did you get that?
Most of us use this:
Energy= h*c/lambda where c is the velocity of light, and lambda is wavelength.