Question

What is the de Broglie wavelength (in meters) of a neutron traveling at a speed of 0.92 c? Since the neutron's speed is close to the speed of light (c), Special Relativity must be used when calculating the linear momentum (p). The mass of the neutron is 1.675 x 10^-27 kg.

Suppose that an alpha particle (m_αα = 6.646 x 10^-27 kg) has a kinetic energy of 75 keV. What is the alpha particle's speed (v) (in terms of "c")? You can determine this by using the Classical Physics equation for kinetic energy and solving for the speed (v). But how do we know if this is correct? How do we know whether or not we need to use Special Relativity? If you use the Classical Physics equation and get a speed that is near the speed of light (or greater --- which is impossible), then you know that Special Relativity is needed in order to solve problems with an alpha particle at a 75 keV energy.

What is the de Broglie wavelength (in meters) of an alpha particle that has a kinetic energy of 75 keV? If Classical Physics equations can be used (as determined above), then you can calculate the linear momentum (p) from the kinetic energy equation K = p²/2m.

If you want to “see” very small objects with an electron microscope, you have to use electrons with a wavelength that is close to the size of the object. What linear momentum (p) (in kg*m/s) would an electron need in order to “see” an object with a size of 8.5 x 10^-10 m?

What voltage difference (V) (in volts) would an electron have to be accelerated through in order to “see” an object with a size of 8.5 x 10^-10 m? For Classical Physics, remember that the kinetic energy gained by a charge (q) when it is accelerated through a voltage difference (V) is given by K = qV. The kinetic energy can be determined from K = p²/2m, where the linear momentum (p) was determined in the preceding problem.Pay attention to your units
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Answer 1