Question

In: Physics

Alpha particles (mass =6.64 x 10^-27 kg) and a kinetic energy of k=945 keV are projected...

Alpha particles (mass =6.64 x 10^-27 kg) and a kinetic energy of k=945 keV are projected at a target nucleus. If the alpha particles have a de broglie wavelength with the same valje as a the diameter of the target nucleus, defermine the radius of the rarget nucleus.

Expert Solution

Given : Mass of Alpha particle = 6.64 * 10-27 kg

Kinetic energy of Alpha particle = 945 keV = 945 * 1.6 * 10-16 J = 1.5 * 10-13 J

The de broglie wavelength can be written as

We also know that the expression for kinetic energy

Put the value of mv from equation(1) in equation(2)

We will find the value of as it is given that de broglie wavelength has same value as the diameter of the target nucleus.

Since, is equal to the diameter of the target nucleus

where r = radius of targeted nucleus

Hence, the radius of targeted nucleus is 7.5 * 10-15 m

genius_generous answered 2 years ago

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