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.

v 154.9= 0.9 length length s little over 154.9cm

the total distance that martina travels that day is

(distance from home to mom's office) plus (distance from mom's office to school)

plus (distance from school to library) plus (distance from library to friend's house)

plus (distance from friend's house to martina's house).

(we don't know what any of these distance actually is.)