A metal target with atomic number Z=46 is bom | vedclass

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

Question

(A) The wavelength of the $K_\alpha$ line is given by Moseley's law: $\frac{1}{\lambda_{K_\alpha}} = R(Z-1)^2 \left( \frac{1}{1^2} - \frac{1}{2^2} \ri

Vedclass · Accepted Answer

$2.53$

Vedclass · Answer

(A) The wavelength of the $K_\alpha$ line is given by Moseley's law: $\frac{1}{\lambda_{K_\alpha}} = R(Z-1)^2 \left( \frac{1}{1^2} - \frac{1}{2^2} ight) = R(Z-1)^2 \left( \frac{3}{4} ight)$.The cut-off wavelength $\lambda_0$ is given by $\lambda_0 = \frac{hc}{eV}$,where $V$ is the accelerating potential of the electron beam.Given the ratio $r = \frac{\lambda_{K_\alpha}}{\lambda_0} = 2$ for $Z_1 = 46$.From the expression for $\lambda_{K_\alpha}$,we see that $\lambda_{K_\alpha} \propto \frac{1}{(Z-1)^2}$.Since the accelerating potential $V$ is the same,$\lambda_0$ remains constant. Therefore,$r \propto \frac{1}{(Z-1)^2}$.Thus,$\frac{r_2}{r_1} = \frac{(Z_1-1)^2}{(Z_2-1)^2}$.Substituting the values: $\frac{r_2}{2} = \frac{(46-1)^2}{(41-1)^2} = \frac{45^2}{40^2} = \left( \frac{9}{8} ight)^2 = \frac{81}{64} = 1.2656$.$r_2 = 2 	imes 1.2656 = 2.5312 \approx 2.53$.

Similar Questions

If $\lambda_{Cu}$ is the wavelength of the $K_{\alpha}$ $X$-ray line of copper (atomic number $Z = 29$) and $\lambda_{Mo}$ is the wavelength of the $K_{\alpha}$ $X$-ray line of molybdenum (atomic number $Z = 42$),then the ratio $\frac{\lambda_{Cu}}{\lambda_{Mo}}$ is close to:

On increasing the number of electrons striking the anode of an $X-$ray tube,which one of the following parameters of the resulting $X-$rays would increase?

$X$-rays can be used to study crystal structure if the wavelength lies in the range:

Molybdenum is used as a target element for the production of $X-$rays because it is

The minimum wavelength of $X$-rays produced in a Coolidge tube operating at $40 \ kV$ is ..... $\mathring A$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module