Cyberphysics - Question on Radioactive Decay

Question on Radioactive Decay

The half-life of radioactive zinc is 50 hours. Find the percentage loss of activity which occurs for a sample each hour.

N_t = XN₀ where X = percentage of radioisotope remaining undecayed

t = 1 hour

half life = 50 hours

l = ln2/(half life) = 0.693/50 hours^-1= 0.01386 hours^-1

X = e^-^lt

Take logs

ln X = -lt

Substitute for l

ln X = - 0.01386 x 1 = -0.01386

Look up the antilog

X = 0.986

percentage undecayed = 98.6%

therefore percentage decayed = 1.4%

loss of activity after 1 hour = 1.4%