In the form of radioactive decay known as alpha decay, an unstable nucleus emits

Question

In the form of radioactive decay known as alpha decay, an unstable nucleus emits a helium-atom nucleus, which is called an alpha particle. An alpha particle contains two protons and two neutrons, thus having mass m=4u and charge q=2e. Suppose a uranium nucleus with 92 protons decays into thorium, with 90 protons, and an alpha particle. The alpha particle is initially at rest at the surface of the thorium nucleus, which is 15 fm in diameter.

A)What is the speed of the alpha particle when it is detected in the laboratory? Assume the thorium nucleus remains at rest.

cm apart with a 27kV potential difference between them. The electrons enter through a small hole in the negative plate, accelerate, then exit through a small hole in the positive plate. Assume that the holes are small enough not to affect the electric field or potential.

A)What is the electric field strength between the plates?E=

Explanation / Answer

cm apart with a 27kV potential difference between them. The electrons enter through a small hole in the negative plate, accelerate, then exit through a small hole in the positive plate. Assume that the holes are small enough not to affect the electric field or potential.

A)What is the electric field strength between the plates?E=

B)With what speed does an electron exit the electron gun if its entry speed is close to zero?

KE = 1/2 mV^2

solving for V

V = sqrt( 2 KE / m)

substituting values we get

V = sqrt(2*27E3 *1.6E-19/9.11E-31) = 9.74E+07 m/s

where I used the conversion 1 eV = 1.6E-19 Joules. The value for the speed is less than 1/3 the speed of light so a relativistic correction is really not necessary. If you insist on treating these electrons as relativistic, then you have to use the following equation for the kinetic energy

KE = mc^2 - moc^2 = mo c^2( 1/sqrt(1-V^2/c^2) - 1)

solving for V we get

V = c sqrt(1 - 1/ (KE / mo c^2 +1)^2)

substituting values

V = 3E8*sqrt(1 - 1/ (27E3*1.6E-19 / (9.11E-31*3E8*3E8) +1)^2)

V = 9.37E+07 m/s

the electric field strength is

E = 27/1.5E-2 = 1800 kV/m

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