Assuming that the smallest measurable wavelength in an experiment is 0.950 fm , what is the maximum mass of an object traveling at 241 m ⋅ s − 1 for which the de Broglie wavelength is observable?

The maximum mass is

Explanation:

The wavelength of the electron can be determined by means of the De Broglie equation.

(1)

Where h is the Planck's constant and p is the momentum.

 (2)

Where m is the mass and v is the velocity.

Before using equation 2 it is necessary to express the wavelength from femtometers to meters.

--

Finally, equation 2 can be used.

But

Hence, the maximum mass is

0.0289 x 10⁻¹⁹kg

The de Broglie wavelength, λ, of a particle varies inversely with the momentum (the product of the mass, m, and velocity, v) of the particle. i.e

λ ∝

λ =            ------------------------(i)

Where;

h = constant of proportionality called Planck's constant = 6.626 x 10⁻³⁴Js

From the question;

λ = 0.950fm = 0.950 x 10⁻¹⁵m

v = 241ms⁻¹

Substitute these values into equation (i) as follows;

0.950 x 10⁻¹⁵ =

Solve for m;

m =

m = 0.0289 x 10⁻¹⁹kg

Therefore, the maximum mass of the object is 0.0289 x 10⁻¹⁹kg

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