Question

An evacuated tube uses an accelerating voltage of 21 kV to accelerate electrons to hit a copper plate and produce X-rays. How much voltage would be required to cause protons to reach the same speed an electron reaches? (We don't worry that the protons would be going in the opposite direction) Group of answer choices

Answer 1

Step-by-step explanation:

It is given that,

Voltage to accelerate electrons to hit a copper plate and produce X-rays,
`V_1=21\ kV=21* 10^3\ V`

Using the conservation of energy for the electrons as :

`21* 10^3=(1)/(2)mv^2`

`v=\sqrt{(2V)/(m)}`

m is the mass of electron

`v=\sqrt{(2* 21* 10^3)/(9.1* 10^(-31))}`

`v=2.14* 10^(17)\ m/s`

For the proton, mass,
`m'=1.67* 10^(-27)\ kg`

Now using the conservation of energy for the protons. We get :

`V=E=(1)/(2)m'v^2`

`V=(1)/(2)* 1.67* 10^(-27)* (2.14* 10^(17))^2`

`V=3.82* 10^7\ volts`

Hence, this is the required solution.