Question

${}_{80}^{197}$Hg decays to ${}_{79}^{191}$Au through electron capture with a decay constant of 0.257 per day. (a) What other particle or particles are emitted in the decay ? (b) Assume that the electron is captured from the K shell. Use Moseley's law $\sqrt{v}$ = a(Z-b) with a = 4.95 $\times {10}^7{s}^{-\frac{1}{2}}$ and b= 1 to find the wavelength of the $K_{\alpha }$ X-ray emitted following the electron capture.

Answer 1

(a) p + e $\to$ n = v neutrino

(b) $\sqrt{f}$ = a (z-b)

$\sqrt{\frac{c}{\lambda }}=\mathrm{4.9.5}\times {10}^7(79-1)$

= $4.95\times {10}^7\times 78$

$\frac{c}{\lambda }=(4.95\times 78{)}^2\times {10}^{14}$

$\lambda =\frac{3\times {10}^8}{149032\times {10}^{14}}$

= $2\times {10}^5\times {10}^{-5}$

= $2\times 1m$= 20 pm