Question

Characteristic of $X$-rays wavelength are related to atomic number by the relation $\sqrt{v}=a(Z-b)$, where $Z$ is atomic number and $a,b$ are constants. If ${\lambda }_1=2.886\mathring{A}$ and ${\lambda }_2=2.365\mathring{A}$ corresponds to $Z_1=55$ and $Z_2=60$ respectively. What is the value of $Z$ for corresponding $\lambda =2.660\mathring{A}$ ?

• A. $7$
• B. $57$
• C. $68$
• D. $32$

Answer 1

Answer: (B)

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