Question

X-rays are incident on a target metal atom having 30neutrons. The ratio of radii of nucleus to that of Helium nucleus is ${14}^{1/3}$ .
(a) Find the atomic number of target atom.
(b) Find the frequency of $K_{\alpha }$ line emitted by this metal.
$R=1.1\times {10}^7{m}^{-1},c=3\times {10}^{8}m/s$.

• A. $20$, $1.546\times {10}^{4}Hz$
• B. $24$, $1.546\times {10}^{1}0Hz$
• C. $26$, $1.546\times {10}^{1}8Hz$
• D. None of these

Answer 1

Answer: (C)

$26$, $1.546\times {10}^{1}8Hz$

Radius of nucleus $\propto A^{1/3}$

$⟹\frac{r_Z}{r_{He}}=\frac{(Z+30{)}^{1/3}}{4^{1/3}}={14}^{1/3}$

$⟹Z=26$