What is the de Broglie wavelength, in meters, associated with a proton. (mass = 1.673 x 10^-24g) accelerated to a velocity of 4.5 x 10^7 m/s? I tried dividing the mass by the velocity. I also multiplied the mass times the velocity, and neither answer came out correctly.
The final answer is 8.8 x 10^-15. My calculater does not allow me to type in figures after 8 decimal points so I am unable to figure out what I am doing wrong.
wavelength = h/mv
h is Planck's constant in Joule-sec.
m is mass in KILOGRAMS (not grams).
v is velocity in m/s.
8.8 x 10^-15 meters is the right answer.
To calculate the de Broglie wavelength associated with a proton, you need to use the de Broglie wavelength formula:
λ = h / p
Where λ is the de Broglie wavelength, h is Planck's constant (approximately 6.626 x 10^-34 J·s), and p is the momentum of the proton.
The momentum of the proton can be calculated using the formula:
p = mv
Where p is the momentum, m is the mass of the proton, and v is the velocity of the proton.
In this case, the mass of the proton is given as 1.673 x 10^-24 g. However, it is important to convert the mass to kilograms before using it in the calculation. So, the mass in kilograms is:
m = 1.673 x 10^-24 g = 1.673 x 10^-27 kg
Next, we need to calculate the momentum of the proton using its mass and velocity. The velocity is given as 4.5 x 10^7 m/s. So, the momentum can be calculated as:
p = (1.673 x 10^-27 kg) x (4.5 x 10^7 m/s)
Now, we can substitute the value of momentum (p) in the de Broglie wavelength formula:
λ = (6.626 x 10^-34 J·s) / [(1.673 x 10^-27 kg) x (4.5 x 10^7 m/s)]
Simplifying this expression will give us the de Broglie wavelength associated with the proton.
Note that dividing the mass by the velocity, as you tried to do, will not give you the correct answer because the de Broglie wavelength formula involves both mass and velocity in the calculation.
I hope this helps!