/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 31 An \(x\)-ray tube operating at \... [FREE SOLUTION] | 91影视

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Chapter 19: Problem 31

An \(x\)-ray tube operating at \(30 \mathrm{kV}\), will emit \(x\)-ray of minimum wavelength (A) \(2840 \AA\) (B) \(0.414 \AA\) (C) \(2.14 \AA\) (D) \(1.78 \AA\)

Short Answer

Expert verified
The minimum wavelength of the X-ray emitted by the tube operating at 30 kV can be calculated using the Duane-Hunt Law formula: \( \lambda_{min} = \dfrac{12.4}{V} \). Plugging in the given voltage, we get \( \lambda_{min} = \dfrac{12.4}{30} = 0.413333 \dotso \AA \). The closest option to this value is option (B) \( 0.414 \AA \). Therefore, the correct answer is (B) \( 0.414 \AA \).

Step by step solution

01

Given Parameters

The operating voltage of the X-ray tube is 30 kV.
02

Compute the minimum wavelength

We will use the Duane-Hunt Law formula, \( \lambda_{min} = \dfrac{12.4}{V} \), where V is the operating voltage in kilovolts. In this case, V = 30 kV. So, \( \lambda_{min} = \dfrac{12.4}{30} = 0.413333 \dotso \AA \)
03

Choosing the correct option

Given the calculated value of \( \lambda_{min} = 0.413333 \dotso \AA \), we can see that the closest option is option (B) \( 0.414 \AA \). So, the correct answer is (B) \( 0.414 \AA \).

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