Question

Hard X-rays for the study of fractures in bones should have a minimum wavelength of ${10}^{11}m$. The accelerating voltage for electrons in X-ray machine should be

• A. $<124.2kV$
• B. $>124.2kV$
• C. Between $60kV$ and $70kV$
• D. $=100kV$

Answer 1

Answer: (A)

$<124.2kV$

Given:-

${\lambda }_{min}={10}^{-11}m$

Solution:-

We know the formula for minimum wavelength of $X$-ray ${{}^{\prime }\lambda }_{mi{n}^{\prime }}$ in an $X$ -ray tube (Bremstrahlung)

${\lambda }_{min}=\frac{hc}{eV}$

Where,

$h$= Planck's constant ,$e$= charge of electron

$C$=speed of light , $V$= accelerating potential

$\Rightarrow V=\frac{hc}{e{\lambda }_{min}}=\frac{6.63\times {10}^{-34}\times 3\times {10}^8}{1.6\times {10}^{-19}\times {10}^{-11}}=124.2\times {10}^{3}V$