Question

The characteristic $X$-rays wavelength is related to atomic number by the relation
$\sqrt{\nu }=a\left(Z-b\right)$
When $Z$ is the atomic number, a and b are Mosley's constants. If ${\lambda }_1=2.886Å$ and ${\lambda }_2=2.365Å$ corresponding to $Z_1=55$ and $Z_2=60$ respectively, the value of Z corresponding to $\lambda =2.660Å$ is

• A. 63
• B. 67
• C. 74
• D. 57

Answer 1

Answer: (D)

$\sqrt{v}=a(Z-b)$
$\sqrt{\frac{c}{\lambda }}=a(Z-b)$
$\therefore \sqrt{\frac{c}{2.886}}=a(55-b)$
$\sqrt{\frac{c}{2.365}}=a(60-b)$
$a=67.5$
$b=7.235$
Now, $\sqrt{\frac{c}{2.660}}=67.5(Z-7.235)$
$Z=57$