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 $\lambda _{1}= \, 2.886 \, Å$ and $\lambda _{2}= \, 2.365 \, Å$ corresponding to $Z_{1}=55$ and $Z_{2}=60$ respectively, the value of Z corresponding to $\lambda =2.660 \, Å$ 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, $\sqrt{\frac{ c }{2.660}}=67.5( Z -7.235)$
$Z =57$