Assuming that the smallest measurable wavelength in an experiment is 0.330 fm(femtometers), what is the maximum mass of an object traveling at 157 m·s^–1 for which the de Broglie wavelength is observable?
mass = ? kg
Chemistry - DrBob222, Monday, October 29, 2012 at 12:29am
wavelength = h/mv
Substitute wavelength (in meters) with v = m/s and solve for mass in kg.
Chemistry - Anonymous, Tuesday, October 30, 2012 at 1:02pm
I don't get the equation.
wavelength is given to you as 0.330 fm. You convert that to meters. 1E15 fm = 1m
h is Planck's constant = 6.6262E-34 J.s
m = mass in kg
v = velocity in m/s
The equation used to calculate the de Broglie wavelength is as follows:
wavelength = h / (m * v)
where:
- wavelength is the de Broglie wavelength
- h is Planck's constant (6.626 x 10^-34 Js)
- m is the mass of the object
- v is the velocity of the object
To find the maximum mass for which the de Broglie wavelength is observable, we need to rearrange the equation to solve for mass (m):
mass = h / (wavelength * v)
Now we can plug in the given values:
wavelength = 0.330 fm = 0.330 x 10^-15 m (converting femtometers to meters)
v = 157 m/s (given velocity)
Substituting these values into the equation, we get:
mass = (6.626 x 10^-34 Js) / (0.330 x 10^-15 m * 157 m/s)
Now we can simplify the equation and calculate the mass:
mass = (6.626 x 10^-34 Js) / (0.330 x 10^-15 m * 157 m/s)
= 1.295 x 10^-55 kg
Therefore, the maximum mass of an object traveling at 157 m/s for which the de Broglie wavelength is observable is 1.295 x 10^-55 kg.