An electron emitted in the beta decay of bismuth-210 has a mean kinetic energy of 390 kev. (a) find the de broglie wavelength of the electron. (b) would such an electron be useful in a davisson-germer type scattering experiment? address this question by determining the angle at which a first-order diffraction maximum would be found using the same nickel target as davisson and germer.

λ=1.7pm

This electron would not be useful in a Davisson-Germer type scattering experiment.

θ=0.45⁰

Explanation:

a) We need to use the relativistic for of the kinetic energy:

.                                   (1)

Here m₀ is the mass rest and c the speed of light in vacuum.

We can write this equation in terms of the linear momentum (p) using this expression:    (2)

if we solve this equation for p and put into the first equation we will have the KE in terms of p.

From (2) we have:      (3)

Let's substitute mc² in (1).

        (4)

Now, let's solve this for p:

And finally, using the De Broglie wavelength equation.

b) To determine the angle of the first order diffraction, we use the Bragg equation:

Now , in the Davisson and Germer, they use a nickel target, so the inter atomic distance for this particular element is around 0.215 nm. We take n=1 for the first order

and .

If we see, this angle is to small to implement the experiment, so it would not be useful in a Davisson-Germer type scattering experiment.

explanation:

the masses of the objects and the distance between them