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.

The equation being referred to here is the de Broglie wavelength equation:

wavelength = h / (mv)

where:
- wavelength is the de Broglie wavelength of the object (in meters)
- h is the Planck's constant (6.62607015 x 10^-34 J·s)
- m is the mass of the object (in kilograms)
- v is the velocity of the object (in meters per second)

To find the maximum mass of an object for which the de Broglie wavelength is observable, we need to use the smallest measurable wavelength (0.330 fm) and the given velocity (157 m·s^–1).

First, let's convert the smallest wavelength from femtometers (fm) to meters (m). Since 1 fm = 1 x 10^-15 m, the smallest wavelength is 0.330 x 10^-15 m.

Now we can plug this value into the equation and solve for mass:

0.330 x 10^-15 m = (6.62607015 x 10^-34 J·s) / (m * 157 m·s^–1)

To solve for mass, we isolate it on one side of the equation:

m = (6.62607015 x 10^-34 J·s) / (0.330 x 10^-15 m * 157 m·s^–1)

Simplifying the equation gives:

m = (6.62607015 x 10^-34 J·s) / (0.330 x 10^-15 m * 157 m·s^–1)

m = 3.99 x 10^-17 kg

So, the maximum mass of an object traveling at 157 m·s^–1 for which the de Broglie wavelength is observable is approximately 3.99 x 10^-17 kilograms.