Chapter 38: Q.69 (page 1117)

The electrons in a cathode-ray tube are accelerated through a $250 V$ potential difference and then shot through a 33-nm-diameter circular aperture. What is the diameter of the bright spot on an electron detector $1.5 m$ behind the aperture?

Short Answer

Expert verified

The short answer of this sum is

Δ y = 8.6 \cdot 10^{- 3} m = 8.6 mm

Step by step solution

Step: 1 Given information

The diameter of the bright spot on an electron detector $1.5 m$

Figure shown below

Calculation

We can begin by focusing on energy conservation.

$E_{k} = U \frac{m v^{2}}{2} = e Δ V v = \sqrt{\frac{2 e Δ V}{m}} λ = \frac{h}{m v} λ = \frac{h}{m \sqrt{\frac{2 e Δ V}{m}}} \sin θ = 1.22 \frac{λ}{D} θ = \arcsin 1.22 \frac{λ}{D} θ = \arcsin 1.22 \frac{\frac{h}{m \sqrt{\frac{2 \cdot Δ V}{m}}}}{D}$

From a picture and simple geometry, we can write.

$Δ y = 2 L \tan θ Δ y = 2 L tanarcsin 1.22 \frac{\frac{h}{m \sqrt{\frac{2 e Δ V}{m}}}}{D} Δ y = 2 \cdot 1.5 \cdot tanarcsin 1.22 \frac{\frac{6.63 \cdot 10^{- 34}}{9.11 \cdot 10^{- 31 \cdot} \sqrt{\frac{2 \cdot 1.6 - 10^{- 19 \cdot 250}}{9.11 \cdot 10^{- 31}}}}}{33 \cdot 10^{- 9}} Δ y = 8.6 \cdot 10^{- 3} m = 8.6 mm$

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The electrons in a cathode-ray tube are accelerated through a $250 V$ potential difference and then shot through a 33-nm-diameter circular aperture. What is the diameter of the bright spot on an electron detector $1.5 m$ behind the aperture?

Short Answer

Step by step solution

Step: 1 Given information

Figure shown below

Calculation

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The electrons in a cathode-ray tube are accelerated through a 250Vpotential difference and then shot through a 33-nm-diameter circular aperture. What is the diameter of the bright spot on an electron detector 1.5mbehind the aperture?

Short Answer

Step by step solution

Step: 1 Given information

Figure shown below

Calculation

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Conservation of Energy and Momentum

Electric Charge Field and Potential

Astrophysics

Dynamics

Kinematics Physics

Circular Motion and Gravitation

Study anywhere. Anytime. Across all devices.

The electrons in a cathode-ray tube are accelerated through a $250 V$ potential difference and then shot through a 33-nm-diameter circular aperture. What is the diameter of the bright spot on an electron detector $1.5 m$ behind the aperture?