Question

If the shortest wavelength of the continuous X-ray spectrum coming out of a Coolidge tube is $0.01nm$, then the de Broglie wavelength of the electron reaching the target metal in the Coolidge tube is approximately
$(hc=12400eVA,h=6.63\times {10}^{-34}$ in MKS, mass of electron$=9.1\times {10}^{-31}kg)$

• A. $0.35$
• B. $0.035$
• C. $35$
• D. $1350$

Answer 1

The correct option is B $0.035$

The shortest wavelength of the continuous X-ray spectrum coming out of a Coolidge tube is $0.01nm$.

So, ${\lambda }_{min}=\frac{12400}{V}\Rightarrow V=\frac{1240}{0.01}=124000volts$

The de Broglie wavelength of the electron reaching the target metal in the Coolidge tube is approximately
$\Rightarrow \lambda =\sqrt{\frac{150}{V}}=0.035$