Question

4. Use Einstein's equivalence of mass and energy to calculate the amount of energy that might be released by beta decay of potassium-40 in a 10.000 sample of KCl, assuming that it decays completely. You will need its nuclear equation and these experimental data for the calculation Mass of an electron (beta particle): 0.0005 AMU Mass of potassium-40: 39.9640 AMU Mass of calcium-40: 39.9626 AMU

Answer 1

The nuclear equation is:

$_{19}^{40}K\rightarrow _{20}^{40}Ca+_{-1}^{0}\beta$

Where a beta particle is an electron.

The number of moles of K we start with is:

$n=\frac{10.00g}{39.9640g/mol}=0.2502\: moles$

So we obtain the same number of moles of Ca and beta particles, which are equivalent to a mass of:

$m=0.2502\: moles\cdot 39.9626\: \frac{g}{mol}+0.2502\: moles\cdot 0.0005\: \frac{g}{mol}=9.9998\: g$

The difference, which is 0.0002 g is released as energy:

$\Delta E=\Delta m\cdot c^{2}=2x10^{-7}kg\cdot (299792458\frac{m}{s})^{2}=2.024x10^{10}\: J$