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

Which one of the following statements is $WRONG$ in the context of $X$-rays generated from an $X$-ray tube?

The potential difference between the cathode and the target in a Coolidge tube is $100 \ kV$. The minimum wavelength of the $X$-rays emitted by the tube is

When $X$-rays from a Coolidge tube pass through an aluminum foil of thickness $0.3 \, mm$,$50\%$ of the $X$-rays are transmitted. If the potential difference between the target and the cathode is increased,the fraction of $X$-rays transmitted through the same foil will be .......

The wavelength of $X-$rays is of the order of

If the energy of a $K$-shell electron is $-40000 \ eV$ and a potential of $60000 \ V$ is applied to a Coolidge tube,which of the following $X$-rays will be formed?

Vedclass Test Series

Exam Paper Generator

Online Exam Module