Approved Tutor Answer1 Year agoTo find the speed of a conduction electron in copper with a kinetic energy of 4.2 eV, we can use the relationship between kinetic energy and speed. The kinetic energy (KE) of an electron can be expressed using the formula:
The kinetic energy of an electron is given by the equation:
KE = (1/2)mv²
Where:
Since the kinetic energy is given in electronvolts (eV), we need to convert it to joules. The conversion factor is:
1 eV = 1.602 x 10-19 J
Thus, to convert 4.2 eV to joules:
KE = 4.2 eV × 1.602 x 10-19 J/eV = 6.72 x 10-19 J
Now that we have the kinetic energy in joules, we can rearrange the kinetic energy formula to solve for speed:
v = sqrt((2 * KE) / m)
Substituting the values we have:
Plugging these into the equation:
v = sqrt((2 * 6.72 x 10-19 J) / (9.11 x 10-31 kg))
Calculating the numerator:
2 * 6.72 x 10-19 J = 1.344 x 10-18 J
Now, dividing by the mass:
1.344 x 10-18 J / 9.11 x 10-31 kg ≈ 1.477 x 1012 m²/s²
Finally, taking the square root gives us the speed:
v ≈ sqrt(1.477 x 1012) ≈ 1.216 x 106 m/s
Therefore, the speed of the conduction electron in copper at near absolute zero with a kinetic energy of 4.2 eV is approximately 1.22 x 106 m/s.
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