Question

The minimum wavelength of X-rays emitted from an X-ray tube operating at a voltage of ${10}^{4}V$ is roughly equal to

• A. $1.23\stackrel{\circ }{A}$
• B. $1.52\stackrel{\circ }{A}$
• C. $2\stackrel{\circ }{A}$
• D. $2.5\stackrel{\circ }{A}$

Answer 1

The correct option is A

$1.23\stackrel{\circ }{A}$

We know that, ${\nu }_{max}=\frac{eV}{h}$
Since ${\nu }_{max}=\frac{c}{{\lambda }_{min}}$, we have ${\lambda }_{min}=\frac{c}{{\nu }_{max}}=\frac{ch}{eV}=\frac{3\times {10}^8\times 6.6\times {10}^{-34}}{1.6\times {10}^{-19}\times {10}^4}=1.23\times {10}^{-10}m=1.23\stackrel{\circ }{A}$
Hence, the correct choice is (a).