An electron and a proton are both moving such that their kinetic energy is roughly 100 eV.How do the speeds of the particles compare?
A)The electron is moving about 30 times faster than the proton.
B)The electron is moving about 1000 times faster than the proton.
C)The electron and proton are moving about the same speed.
D)The proton is moving about 30 times faster than the electron.

Question

Quizplus · Accepted Answer

The kinetic energy of a particle is given by:

KE = 1/2 mv^2

where m is the mass of the particle and v is its speed. Since the kinetic energy is the same for both the electron and proton, we can write:

1/2 m_e v_e^2 = 1/2 m_p v_p^2

where m_e and m_p are the masses of the electron and proton, respectively.

Simplifying by dividing both sides by 1/2 and taking the square root, we get:

v_e = sqrt(v_p^2 * (m_p/m_e))

Since m_p/m_e is roughly 1836 (the mass of a proton is about 1836 times that of an electron), we can approximate the above equation as:

v_e ≈ 43 v_p

Therefore, we conclude that the electron is moving about 43 times faster than the proton. Since the choices only differ by a factor of 30, the closest answer is A), which says that the electron is moving about 30 times faster than the proton.

An Electron and a Proton Are Both Moving Such That