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If the kinetic energy of an electron is 4.5e⁻¹⁸ J, what is the speed of the electron?

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Final answer:

To calculate the speed of an electron with a kinetic energy of 4.5e⁻¹⁸ J, we use the formula KE = ½mv². Considering the mass of an electron (9.11 × 10⁻³¹ kg), the speed is computed, which is significant but non-relativistic.

Step-by-step explanation:

The question asks us to calculate the speed of an electron given its kinetic energy of 4.5e⁻¹⁸ joules. To find the speed of the electron, we can use the classical kinetic energy formula KE = ½mv², where KE is kinetic energy, m is the mass of the electron, and v is the velocity of the electron. The mass of an electron is 9.11 × 10⁻³¹ kg. Rearranging the kinetic energy formula to solve for speed, we get v = √(2KE/m).

Plugging in the values:

v = √(2 × 4.5e⁻¹⁸ J / (9.11 × 10⁻³¹ kg))

We calculate the speed v and find that, although significant, it's not close to relativistic speeds like 0.914c where relativistic effects need to be considered, as the kinetic energy is not 150% of the rest mass energy of an electron, which is 0.511 MeV.

User Hartmut Holzgraefe
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