Question

In a microwave oven, electrons describe circular motion in a magnetic field within a special tube called amagnetron; as you'll learn in Chapter 29, the electrons' motion results in the production of micowaves. The electrons circle at a frequency of 2.15 GHz . The magnetron can accommodate electron orbits with maximum diameter 2.62 mm .

Part A

What's the magnetic field strength?

Part B

What's the electrons' energy in eV.

Answer 1

The magnetic field strength and the electrons' energy are 0.077 T and 0.8906 eV.

Step-by-step explanation:

Given that,

Diameter = 2.62 mm

Frequency = 2.15 GHz

(A). We need to calculate the magnetic field strength

Using formula of the magnetic field strength

`B=(2\pi mf)/(e)`

Where, f = frequency

e = charge of electron

Put the value into the formula

`B=(2*3.14*9.1*10^(-31)*2.15*10^(9))/(1.6*10^(-19))`

`B=0.077\ T`

(B). We need to calculate the energy of electron

Using formula of energy

`E=(1)/(2)m(r\omega)^2`

`E=(1)/(2)*9.1*10^(-31)*(1.31*10^(-3)*2\pi*2.15*10^(9))^2`

`E=1.4249*10^(-16)\ J`

The energy in eV

`1 eV=1.6*10^(-16)\ J`

`E=(1.4249*10^(-16))/(1.6*10^(-16))`

`E=0.8906\ eV`

Hence, The magnetic field strength and the electrons' energy are 0.077 T and 0.8906 eV.