When 5×1012 photons pass through an experimental apparatus, 2.0×109 land in a 0.10-mm-wide strip. What is the probability density at this point?

Ch 39: Wave Functions and Uncertainty

Knight Calc - Physics for Scientists and Engineers 5th Edition

Knight Calc5th EditionPhysics for Scientists and EngineersISBN: 9780137344796당신이 사용하는 게 아니라요?교과서 변경

모든 교과서

Knight Calc 5th Edition

Ch 39: Wave Functions and Uncertainty

문제 9

39장, 문제 9

When 5×10¹² photons pass through an experimental apparatus, 2.0×10⁹ land in a 0.10-mm-wide strip. What is the probability density at this point?

검증된 단계별 안내

Step 1: Understand the problem. The probability density is defined as the probability per unit area. To calculate it, we need to determine the fraction of photons that land in the specified strip and divide it by the area of the strip.

Step 2: Calculate the fraction of photons that land in the strip. This is given by the ratio of the number of photons landing in the strip to the total number of photons: \( \text{Fraction} = \frac{2.0 \times 10^9}{5.0 \times 10^{12}} \).

Step 3: Determine the area of the strip. The width of the strip is given as \( 0.10 \ \text{mm} \), which needs to be converted to meters: \( 0.10 \ \text{mm} = 0.10 \times 10^{-3} \ \text{m} \). Assume the length of the strip is \( 1 \ \text{m} \) (if not specified, this is a common assumption for such problems). Thus, the area is \( \text{Area} = \text{Width} \times \text{Length} = (0.10 \times 10^{-3}) \times 1 \).

Step 4: Calculate the probability density. The probability density is the fraction of photons divided by the area of the strip: \( \text{Probability Density} = \frac{\text{Fraction}}{\text{Area}} = \frac{\frac{2.0 \times 10^9}{5.0 \times 10^{12}}}{(0.10 \times 10^{-3}) \times 1} \).

Step 5: Simplify the expression to find the probability density. Perform the division and simplify the units to express the final result in terms of \( \text{m}^{-2} \).

비슷한 문제에 대한 검증된 영상 답변:

이 영상 해법은 위 문제에 도움이 된다고 튜터들이 추천한 것입니다.

도움이 되었나요?

주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

Photon

A photon is a quantum of electromagnetic radiation, representing the smallest discrete amount of light or other electromagnetic energy. Photons are massless particles that travel at the speed of light and exhibit both wave-like and particle-like properties. Understanding photons is essential for analyzing interactions in experiments involving light and energy transfer.

Probability Density

Probability density refers to the likelihood of finding a particle, such as a photon, in a specific region of space per unit area. It is calculated by dividing the number of particles that land in a given area by the area itself. In this context, it helps quantify how concentrated the photons are in the specified strip, providing insight into their distribution.

Area Calculation

Area calculation is fundamental in physics for determining the spatial extent of a region where events occur, such as the landing of photons. In this scenario, the width of the strip (0.10 mm) must be converted to appropriate units (e.g., square meters) to calculate the probability density accurately. This concept is crucial for relating the number of photons to the area they occupy.