The maximum wavelength of hard X-rays require | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(B) The energy of an $X$-ray photon is given by $E = \frac{hc}{\lambda}$.For the maximum energy (minimum wavelength),the accelerating voltage $V$ is r

Vedclass · Accepted Answer

$> 124.2 \ kV$

Vedclass · Answer

(B) The energy of an $X$-ray photon is given by $E = \frac{hc}{\lambda}$.For the maximum energy (minimum wavelength),the accelerating voltage $V$ is related to the wavelength $\lambda$ by the equation $\lambda = \frac{hc}{eV}$.Substituting the values $h = 6.63 	imes 10^{-34} \ J \cdot s$,$c = 3 	imes 10^8 \ m/s$,and $e = 1.6 	imes 10^{-19} \ C$:$V = \frac{hc}{e\lambda} = \frac{12400 	imes 10^{-10} \ V \cdot m}{10^{-11} \ m} = 124000 \ V = 124 \ kV$.Since the wavelength $\lambda$ is inversely proportional to the voltage $V$ (i.e.,$\lambda = \frac{12400}{V} \ 	ext{Å}$),to obtain a wavelength of $10^{-11} \ m$ (which is $0.1 \ 	ext{Å}$),the voltage must be at least $124 \ kV$.Therefore,the accelerating voltage must be greater than $124 \ kV$ to produce $X$-rays with a wavelength of $10^{-11} \ m$ or shorter.

The maximum wavelength of hard $X$-rays required for the study of bone fractures is $10^{-11} \ m$. The accelerating voltage in the $X$-ray machine must be:

Similar Questions

The wavelength of the ${K_\alpha}$ line for an element of atomic number $29$ is $\lambda$. Then the wavelength of the ${K_\alpha}$ line for an element of atomic number $15$ is (Take Moseley's constant $b = 1$ for both elements).

The minimum frequency $\nu$ of continuous $X$-rays is related to the applied potential difference $V$ as

The minimum wavelength of $X$-rays emitted by an $X$-ray tube is $0.4125 \mathring{A}$. The accelerating voltage is ...... $kV$.

The minimum wavelength of $X$-rays produced by an $X$-ray tube depends on which of the following?

Vedclass Test Series

Exam Paper Generator

Online Exam Module