X rays are emitted when the electrons hit the screen in a cathode ray tube (CRT),i.e.,an old TV set.If the shortest wavelength X ray emitted is 3.7 $\times$ 10^-2 nm,then what is the voltage that the electrons are accelerated through in the TV set? A)2.1 $\times$ 10^-23 V B)34 kV C)27 V D)34 V E)27 kV

Question

Quizplus · Accepted Answer

The energy of the accelerated electrons (in electron volts) can be calculated using the de Broglie wavelength equation:

λ = h/p = h/(√(2mE))

where λ is the wavelength, h is Planck's constant, p is the momentum, m is the mass of the electron and E is the energy.

The shortest wavelength X-ray emitted corresponds to the highest energy electrons, which will have just enough energy to produce X-rays when they hit the screen. Therefore, the energy of these electrons can be calculated using the equation:

hc/λ = √(2meV)

where h and c are constants, λ is the wavelength of the X-ray, and me is the mass of the electron.

Solving for V:

V = [(hc/λ)^2]/(2me)

Plugging in the values given:

V = [(6.626 x 10^-34 J s x 3 x 10^17 m/s) / (3.7 x 10^-12 m)]^2 / (2 x 9.11 x 10^-31 kg)

V = 34 kV

Therefore, the correct answer is B.

X Rays Are Emitted When the Electrons Hit the Screen ×\times×

X Rays Are Emitted When the Electrons Hit the Screen $\times$