Speed of electron in a plane

[missyc8]

Homework Statement

An electron with kinetic energy 1.92 keV circles in a plane perpendicular to a uniform magnetic field. The orbit radius is 26.0 cm.
Find the speed of the electron.

Find the magnetic field.

Find the frequency of circling. (Hz)

Find the period of the motion.

Homework Equations

v=sqrt(2*(3.7E-16J/9.109E-31)
k=(mv)^2/2
B-mvqr

The Attempt at a Solution

for velocity i get 2.85E-23 m/s ...but it is wrong...i do not know what to do

 

[willem2]

The Attempt at a Solution

for velocity i get 2.85E-23 m/s ...but it is wrong...i do not know what to do

try computing sqrt(2*(3.7E-16J/9.109E-31)) again

 

[tomcue]

I would first clarify the units used in the given information. The kinetic energy is given in keV (kiloelectron volts), which is a unit of energy commonly used in atomic and nuclear physics. However, the standard unit for energy in the International System of Units (SI) is joules (J). Therefore, I would convert the given kinetic energy of 1.92 keV to joules by using the conversion factor 1 keV = 1.6022E-16 J. This gives us a kinetic energy of 3.075E-16 J.

Next, I would use the formula for kinetic energy, K=(1/2)mv^2, to solve for the speed of the electron. Since the mass of an electron (m) is known to be 9.109E-31 kg, we can rearrange the formula to solve for velocity (v) and plug in the known values of kinetic energy and mass. This gives us a speed of 2.85E8 m/s for the electron.

To find the magnetic field, we can use the formula B=mvqr, where m is the mass of the electron, v is its velocity, q is its charge (which is known to be -1.6022E-19 C), and r is the orbit radius. Plugging in the known values, we get a magnetic field strength of 2.17E-4 T.

The frequency of circling can be found using the formula f=v/2πr, where v is the speed of the electron and r is the orbit radius. This gives us a frequency of 2.17E5 Hz.

Finally, the period of motion can be found using the formula T=1/f, where T is the period and f is the frequency. Plugging in the previously calculated frequency, we get a period of 4.60E-6 seconds.

It is important to note that the given information does not specify the direction of the magnetic field, so the calculated values may differ depending on the direction chosen. Additionally, the given information does not specify the type of orbit (e.g. circular, elliptical), so the calculated values may also vary depending on the assumed orbit.