This step converts the meters into nanometers. - Salisbury University

First we have to relate the momentum(p) to kinetic energy(KE) We know that:

and that momentum(p) is:

Therefore, we can

rearrange the kinetic energy to incorporate the momentum:

We can then rearrange the equation with respect

to momentum(p):

(1)

Now that we know the momentum we can use the de Broglie equation to determine the wavelenght, but first we have to define the de Broglie equation as:

(2)

Now that we have our equations now we can define the variable from the problem to plug in, but making sure each variable is converted to the correct units:

(3)

(4)

0.4358640000

(5)

(6)

(7) Because the units are in meters, to convert to nanometer we can multiply the wavelength by 10^9 nanometers when we do this we get:

(8)

The significance of this problem shows how velocity relates to wavelengths. This problem demostrates how velocity and wavelengths are inverslry proportional. The mass also has an influence on the wavelength. Like the velocity, the mass is also inversely proportional to the wavelength.

this step converts the meters into nanometers.

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